GIỚI HẠN DÃY SỐ

value of$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}$\lim\frac{3-2n}{3n-2} $$\lim \frac{3-2}{3n-2}$$ bằng

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}$-\frac{2}{3} $$-\frac{}{3}$$

• $\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}$\frac{2}{3} $$\frac{}{3}$$

• $\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}$\frac{3}{2} $$\frac{}{2}$$

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}$-\frac{3}{2} $$-\frac{}{2}$$

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}{{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}$\lim\frac{2n^2-3n+1}{n^2-2n+3} $$\lim \frac{2n^2-3n+}{N^2-2n+3}$$ bằng

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}$2 $$2$$

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}$3 $$3$$

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}$1 $$1$$

• $\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}$4 $$4$$

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}$\lim\frac{-3}{4n^2-2n+1} $$\lim \frac{-}{4n^2-2n+1}$$

• -3/4

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}$-\infty $$-\infty$$

• 0

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}$+\infty $$+\infty$$

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}}{{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}}$\lim\frac{n+2n^2}{n^3+3n-1} $$\lim \frac{N+2n^{}}{N^3+3n-1}$$

• -2

• 1

• 2/3

• 0

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">một</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">.</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">5</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">=</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}$\lim\frac{a.n+4}{5n+3}=2 $$\lim \frac{một.N+}{5n+3}=2$$

• a=10

• a=5

• a=0

• a=4/3

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">5</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}$\lim\frac{n^2-3n^3}{2n^3+5n-2} $$\lim \frac{N^2-3n^{}}{2n^3+5n-2}$$

• -3/2

• 1/5

• 1/2

• 0

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">7</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}$\lim\frac{\left(2n-n^3\right)\left(3n^2+1\right)}{\left(2n-1\right)\left(n^4-7\right)} $$\lim \frac{\left(2n-N^3\right)\left(3n^2+1\right)}{\left(2n-1\right)\left(n^4-7\right)}$$

• -3/2

• 1

• 3

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}$+\infty $$+\infty$$

$\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">lim</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml"></span></span></span></span>\frac{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">3</span></span></span></span>}{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">2</span></span></span></span>}\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">1</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span><span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">(</span></span></span></span>{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">N</span></span></span></span>}}^{\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">4</span></span></span></span>}}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">-</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">7</span></span></span></span>}<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">)</span></span></span></span>}$\lim\frac{\left(2n-n^3\right)\left(3n^2+1\right)}{\left(2n-1\right)\left(n^4-7\right)} $$\lim \frac{\left(2n-N^3\right)\left(3n^2+1\right)}{\left(2n-1\right)\left(n^4-7\right)}$$

• -3/2

• 1

• 3

• $<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">+</span></span></span></span>\mathrm{<span\; class="katex-container"\; data-idx="0"\; contenteditable="false"><span\; class="katex-display"><span\; class="katex"><span\; class="katex-mathml">\infty </span></span></span></span>}$+\infty $$+\infty$$