Evaluating Limits Analytically

 $\lim_{x\rightarrow1}^{ }x^3+3x^2-2x$  

 $\lim_{x\rightarrow-3}\frac{x^2+4x+3}{x^2-3}$  

 $\lim_{x\rightarrow-2}\left(x-6\right)^{\frac{2}{3}}$  

 $\lim_{x\rightarrow1}\frac{x-1}{x^2-1}$  

 $\lim_{x\rightarrow0}\frac{1}{x^2}$  (you can write the solution as a word)

 $\lim_{x\rightarrow2}\frac{x^2+5x+6}{x+2}$  

 $\lim_{x\rightarrow2}\frac{x^2-3x+2}{x^2-4}$  

 $\lim_{x\rightarrow0}\frac{\left(4+x\right)^2-16}{x}$  

 $\lim_{x\rightarrow0}\frac{5x^3+8x^2}{3x^4+12x^2}$  

 $\lim_{x\rightarrow\pi}\frac{\tan x}{\cos x}$