91Ó°ÊÓ

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

$\underset{x→0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}1& ifx<0\\ -1& ifx>0\end{array}\right.$

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$\frac{\mathrm{Ï€}}{4}$

In Problems 7– 42, find each limit algebraically.

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

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

$\underset{x→1^{-}}{\lim }\frac{x^3-x}{x-1}$

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

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

In Problems 7– 42, find each limit algebraically.

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

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

$\underset{x→0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}\sin \left(x\right)& ifx≤0\\ x^2& ifx>0\end{array}\right.$

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

In Problems 41 and 42, a function f is defined over an interval [a, b]

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

(b) Approximate the area A by partitioning [a, b] into three subintervals of equal length and choosing u as the left endpoint of each subinterval.

(c) Approximate the area A by partitioning [a, b] into six subintervals of equal length and choosing u as the left endpoint of each subinterval.

(d) Express area A as an integral.

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

$f\left(x\right)=4-x^2,[-1,2]$

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

$\underset{x→0}{lim}f\left(x\right),f\left(x\right)=\left\{\begin{array}{ll}{e}^x& ifx>0\\ 1-x& ifx≤0\end{array}\right.$