Mathematics

Problem

A differentiable function

h

satisfies

h(5)=-1

and

h'(5)=4

. a. Evaluate

\displaystyle \lim_{x\to 5} \frac{h(x)+1}{x-5}

. Show how the given information about

h

leads directly to the numerical value of the limit. b. Determine

\displaystyle \lim_{x\to 5} h(x)

. Explain your reasoning. c. State whether

h

is continuous at

x=5

and justify your conclusion using results from parts (a) and (b).