91Ó°ÊÓ

Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow 2^{-}} \frac{x+1}{x^{2}-x-2}$$

Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow 1} \sqrt{x^{3}+6 x^{2}+2 x+5}$$

Determine whether or not the function is continuous at the given number. $$f(x)=\left\\{\begin{array}{ll} x^{2}-x & \text { if } x \leq 0 \\ 2 x^{2} & \text { if } x>0 \end{array} \text { at } x=0\right.$$

Use the Infinite Limit Theorem and the properties of limits to find the limit. $$\lim _{x \rightarrow-\infty} \frac{(x-3)(x+2)}{2 x^{2}+x+1}$$

Determine whether or not the function is continuous at the given number. $$g(x)=\left\\{\begin{array}{ll} x^{3}-x+1 & \text { if } x<2 \\ 3 x^{2}-2 x-1 & \text { if } x \geq 2 \end{array} \text { at } x=2\right.$$

Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow 2} \sqrt{x^{2}+x+3}$$

Use the Infinite Limit Theorem and the properties of limits to find the limit. $$\lim _{x \rightarrow \infty} \frac{(2 x+1)(3 x-2)}{3 x^{2}+2 x-5}$$

Use the Infinite Limit Theorem and the properties of limits to find the limit. $$\lim _{x \rightarrow \infty}\left(3 x-\frac{1}{x^{2}}\right)$$

Find the limit if it exists. If the limit does not exist, explain why. $$\lim _{x \rightarrow 1^{+}}(\sqrt{x-1}+3)$$

Determine whether or not the function is continuous at the given number. $$f(x)=|x-3| \text { at } x=3$$