91Ó°ÊÓ

In Problems 13–32, use the accompanying graph of y = f(x).

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Is f continuous at 4?

In Problems 13–32, use the accompanying graph of y = f(x).

Is f continuous at 5?

In Problems 7– 42, find each limit algebraically.

$\underset{x→-3}{\lim }\frac{x^2+x-6}{x^2+2x-3}.$

Consider the function $f\left(x\right)=\sqrt{1-x^2}$whose domain is the interval $[-1,1]$

(a) Graph f.

(b) Approximate the area under the graph of f from $-1$to $1$by dividing $[-1,1]$into five subintervals, each of equal length.

(c) Approximate the area under the graph of f from $-1$to $1$by dividing $[-1,1]$into ten subintervals, each of equal length.

(d) Express the area as an integral.

(e) Evaluate the integral using a graphing utility.

(f) What is the actual area?

In Problems $30–32$, find the slope of the tangent line to the graph of $f$at the given point. Graph $f$and the tangent line

$32.f\left(x\right)=x^3+x^2$at$(2,12)$

Graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x→1}{\lim }f\left(x\right),f\left(x\right)=\ln \left(x\right)$

In Problems 21–32, find the derivative of each function at the given number.

$f\left(x\right)=\cos \left(x\right)$at$0$

In Problems 33–42, use a graphing utility to find the derivative of each function at the given number.

$f\left(x\right)=3x^3-6x^2+2$at$-2$

In Problems $33–35$, find the derivative of each function at the number indicated.

$\text{33.}f\left(x\right)=−4x^2+5$at$3$

In Problems 33– 44, find the one-sided limit.

$\underset{x→1^{+}}{\lim }(2x+3)$