Limits...Intro and Techniques

Given this table, what limits are most accurate?

• As x approaches 3, the limit is infinity

• As x approaches 3, the limit is negative infinity

• As x approaches 3 from the left, the limit is negative infinity & as x approaches 3 from the right, the limit is infinity

• As x approaches 3 from the left, the limit is infinity and as x approaches 3 from the right, the limit is negative infinity

Based on the table, the left and right sides of zero are approaching what y-value?

Determine the limit by direct substitution:  $\lim_{x\rightarrow4}\left(3x-5\right)$ ( Just sub in the value)

• 7

• 2

• -5

• 3

Determine the limit :  $\lim_{x\rightarrow-5}\left(-2x+1\right)$  

Solve using the dividing out technique:  $\lim_{x\rightarrow3}\left(\frac{x^2-9}{x-3}\right)$    Hint:  Factor and reduce and then direct substitution

• 3

• 6

• -3

• 9

Find the limit by the dividing out technique:  $\lim_{x\rightarrow1}\left(\frac{2x^2+x-3}{x-1}\right)$  Hint:  factor

Find the limit:  $\lim_{x\rightarrow-4}\left(\frac{x^2+11x+28}{x+4}\right)$  

Multiply:  $\left(\sqrt{x+3}-2\right)\left(\sqrt{x+3}+2\right)$  

•  $x-3$  

•  $x-2$  

•  $x-1$  

Multiply:  $\left(\sqrt{x}+5\right)\left(\sqrt{x}-5\right)$  Which of the following shows the correction worked solution?

•  $x\ +5\sqrt{x}-5\sqrt{x}-25\ =\ x\ -25$  

•  $x-5\sqrt{x}-5\sqrt{x}-25=\ x-10\sqrt{x}-25$  

•  $x^2-5x+5x-25=x^2-25$  

Multiply:  $\left(\sqrt{x+9}+3\right)\left(\sqrt{x+9}-3\right)$  

• x - 3

• x

• x + 9

• x - 9