91Ó°ÊÓ

Write the integral that represents the shaded area. Do not attempt to evaluate

In Problems 7–16, use a table to find the indicated limit.

$16.\underset{x→0}{\lim }\frac{\tan x}{x},x$in radians.

a function f is defined over an interval $\left[a,b\right]$

(a) Graph f, indicating the area A under f from a to b.

(b) Approximate the area A by partitioning $\left[a,b\right]$

into four subintervals of equal length and choosing u as the left

endpoint of each subinterval.

(c) Approximate the area A by partitioning $\left[a,b\right]$

into eight

subintervals of equal length and choosing u as the left

endpoint of each subinterval.

(d) Express the area A as an integral.

(e) Use a graphing utility to approximate the integral.

$f\left(x\right)=x^3\left[1,5\right]$

In Problems 9–20, find the slope of the tangent line to the graph of f at the given point. Graph f and the tangent line.

$f\left(x\right)=3x^2-x\mathrm{at}\left(0,0\right)$

In Problem, use the accompanying graph of $y=f\left(x\right)$

What is the domain of f?

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

Find the y-intercept(s), if any, of $f$.

In Problems 7– 42, find each limit algebraically

$\underset{x→3}{\lim }(2-5x)$

In Problem, use the accompanying graph of $y=f\left(x\right)$

What is the range of f?

a function f is defined over an interval $\left[a,b\right]$

(a) Graph f, indicating the area A under f from a to b.

(b) Approximate the area A by partitioning $\left[a,b\right]$

into four subintervals of equal length and choosing u as the left

endpoint of each subinterval.

(c) Approximate the area A by partitioning $\left[a,b\right]$

into eight

subintervals of equal length and choosing u as the left

endpoint of each subinterval.

(d) Express the area A as an integral.

(e) Use a graphing utility to approximate the integral.

localid="1647079335733" role="math" $f\left(x\right)=\frac{1}{x}\left[1,5\right]$

A particle is moving along a straight line according to some position function $s\left(t\right)$. The distance (in feet) of the particle, s, from its starting point after t seconds is given in the table. Find the average rate of change of distance from $t=3$to $t=6$seconds