CPM Homework Help : CALC Problem 4-24

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Home > CALC > Chapter 4 > Lesson 4.1.2 > Problem 4-24

4-24.

Determine the following limits quickly.

$\lim\limits_ { x \rightarrow 2 } \frac { x ^ { 2 } - 4 } { x - 2 }$
Hint (a):
Factor first. The denominator might 'cancel out.'

$\lim\limits_ { h \rightarrow 0 } \frac { ( 1 + h ) ^ { 2 } - 1 } { h }$
Hint (b):
This is Hana's definition of a derivative at a point.
$f'(a)=\lim\limits_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h}$
What is $f(x)$ ?
What is $a$ ?
What is $f^\prime(x)$ ?
What is $f^\prime(a)$ ?
Answer (b):
$f(x) = x^2$
$a = 1$
$f^\prime(x) = 2x$
$f^\prime(a) = 2$
Therefore the limit as $h→0 = f^\prime(a) = 2$

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