91Ó°ÊÓ

Find each limit, if it exists. $$\lim _{x \rightarrow-\infty} \frac{-3 x^{2}+5}{2-x}$$

Draw a graph to match the description given. Answers will vary. \(g(x)\) has a positive derivative over \((-\infty,-3)\) and a negative derivative over \((-3, \infty)\)

Find the absolute maximum and minimum values of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, is specified, use the real line, \((-\infty, \infty)\). $$f(x)=(x+1)^{3}$$

Draw a graph to match the description given. Answers will vary. \(f(x)\) has a negative derivative over \((-\infty, 1)\) and a positive derivative over \((1, \infty)\)

Find the absolute maximum and minimum values of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, is specified, use the real line, \((-\infty, \infty)\). $$f(x)=(x-1)^{3}$$

Find each limit, if it exists. $$\lim _{x \rightarrow-2} \frac{x^{3}+8}{x^{2}-4}$$

Find the absolute maximum and minimum values of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, is specified, use the real line, \((-\infty, \infty)\). $$f(x)=2 x-3 ;[-1,1]$$

Find each limit, if it exists. $$\lim _{x \rightarrow \infty} \frac{-6 x^{3}+7 x}{2 x^{2}-3 x-10}$$

Draw a graph to match the description given. Answers will vary. \(F(x)\) has a negative derivative over \((-\infty, 2)\) and (5,9) and a positive derivative over (2,5) and \((9, \infty)\)

Find the absolute maximum and minimum values of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, is specified, use the real line, \((-\infty, \infty)\). $$f(x)=9-5 x ; \quad[-10,10]$$