CPM Homework Help : PC Problem 9-56

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9-56.

Compute the following limits using either a calculator or algebra.

$\lim\limits _ { x \rightarrow 3 } \frac { x ^ { 3 } - 8 } { x ^ { 2 } - 4 }$
Hint (a):
Substitute $3$ in for $x$ .
This can be done because it does not create division by zero.

$\lim\limits _ { x \rightarrow 2 } \frac { x ^ { 3 } - 8 } { x ^ { 2 } - 4 }$
Hint (b):
Substituting $2$ in for $x$ results in division by zero. Factor and simplify, eliminating this issue. Then substitute $2$ in for ' $x$ '.

$\lim\limits _ { h \rightarrow 0 } \frac { f ( 2 + h ) - f ( 2 ) } { h }$ where $f(x)=3x-4$
Step (c):
$\lim\limits_{x\rightarrow 0}\frac{(3(2+h)-4)-((3)(2)-4)}{h}$

$\lim\limits _ { h \rightarrow 0 } \frac { g ( 3 + h ) - g ( 3 ) } { h }$ where $g(x)=\frac{6}{x}$
Step (d):
$\lim\limits_{x\rightarrow 0}\frac{\frac{6}{3+h}-\frac{6}{3}}{h}=\frac{\frac{18-6(3+h)}{3(3+h)}}{h}$

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