CPM Homework Help : PC3 Problem 7-47

CPM Homework Banner

Home > PC3 > Chapter 7 > Lesson 7.1.4 > Problem 7-47

7-47.

Evaluate each of the following expressions.

$\lim\limits _ { x \rightarrow 3 } \frac { x } { x ^ { 2 } + 1 }$
Hint (a):
Use a graph or substitute $3$ into the expression since there is not a division by zero problem.

$\lim\limits _ { x \rightarrow \frac { \pi } { 2 } } \frac { \operatorname { sin } ( x ) } { x }$
Hint (b):
Substitute $\frac{\pi}{2}$ for $x$ in the expression.

$f(3)$ if $f(x)=\frac{x}{x^2+1}$
Step (c):
$f(3)=\frac{3}{3^2+1}$

$g\left(\frac{\pi}{2}\right)$ if $g(x)=\frac{\sin(x)}{x}$
Step (d):
$g(\frac{\pi}{2})=\frac{\sin\left(\frac{\pi}{2}\right)}{\large\frac{\pi}{2}}$

Compare your answers to parts (a) and (c) and parts (b) and (d). What can you conclude about $f$ and $g$ ? Explain.

© 2022 CPM Educational Program. All rights reserved.