CPM Homework Help : CALC Problem 4-130

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Home > CALC > Chapter Ch4 > Lesson 4.4.1 > Problem 4-130

4-130.

Evaluate.

$\lim\limits_ { x \rightarrow 9 } \frac { \sqrt { x } - 3 } { x - 9 }$
Hint 1(a):
You could multiply the numerator and denominator by the conjugate of the numerator.
Hint 2(a):
Or... you could recognize that this is Ana's Definition of the Derivative.

$\lim\limits_ { h \rightarrow 0 } \frac { \sqrt { 2 + h } - \sqrt { 2 } } { h }$
Hint (b):
This is Hana's Definition of the Derivative.
What is $f(x)$ ?
What is $a$ ?
What is $f^\prime(x)$ ?
The limit $= f^\prime(a) =$ _________

$\lim\limits_ { x \rightarrow \infty } \frac { 2 \sqrt { x } + 1 } { 5 - \sqrt { x } }$
Hint (c):
This limit is approaching infinity. What is the end behavior? Is there a horizontal asymptote? Compare the highest-power terms in the numerator and denominator. Pay attention to coefficients.
Answer (c):
$=-2$

$\lim\limits_ { x \rightarrow \infty } \operatorname { cos } x$
Hint (d):
Visualize the graph of $y =\operatorname{cos}x$ . It oscillates as $x→∞$ .

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