91Ó°ÊÓ

In Problems 33–42, use a graphing utility to find the derivative of each function at the given number.
$f\left(x\right)=x^2\sin x$at$\frac{\mathrm{Ï€}}{3}$

In Problems 7– 42, find each limit algebraically.

$\underset{x→2}{\lim }\frac{x^3-2x^2+4x-8}{x^2+x-6}.$

In Problems 1– 6, find each limit

$\underset{x→-1}{\lim }\frac{x^2-4x-5}{x^3+1}$

find the limit$\underset{x→1^{-}}{\lim }\sqrt{1-x^2}$

The area under the graph of f from a to b is denoted by the
symbol ___________.

If a function f has no limit as x approaches c, then we say

that $\underset{x→c}{\lim }f\left(x\right)$__ __ __.

Name the trigonometric functions that have asymptotes.

True or False The limit of a polynomial function as $x$approaches $5$equals the value of the polynomial at $5$

If $\underset{x→c}{\lim }\frac{f\left(x\right)-f\left(c\right)}{x-c}$exists, it is called the _____ of f at c.

The function $f\left(x\right)=2x+3$is defined on the interval role="math" localid="1652696446205" $\left[0,4\right]$.

(a) Graph f.

In (b)–(e), approximate the area A under f from x = 0 to x = 4 as follows:

(b) Partition $\left[0,4\right]$into four subintervals of equal length and choose u as the left endpoint of each subinterval.

(c) Partition $\left[0,4\right]$into four subintervals of equal length and choose u as the right endpoint of each subinterval.

(d) Partition $\left[0,4\right]$into eight subintervals of equal length and choose u as the left endpoint of each subinterval.

(e) Partition $\left[0,4\right]$into eight subintervals of equal length and choose u as the right endpoint of each subinterval.

(f) What is the actual area A?