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8-30.

Recall that $\lim \limits _{x\rightarrow\infty}a^x=∞$ when $a>1$ . Evaluate each of the following limits.

$\lim \limits _ { x \rightarrow \infty } a ( x ) ,$ where $a ( x ) = 3 ^ { x }$
Hint (a):
Sketch a graph.

$\lim \limits _ { x \rightarrow \infty } b ( x ) ,$ where $b ( x ) = 3 ^ { x } - 6 ( 2 ^ { x } )$
Hint (b):
What is the dominant term?

$\lim \limits _ { x \rightarrow \infty } c ( x ) ,$ where $c ( x ) = - 5 ^ { x }$
Hint (c):
Sketch a graph.

$\lim \limits _ { x \rightarrow \infty } d ( x ) ,$ where $d(x)=$ $-5^x+10(4^x)$
Hint (d):
What is the dominant term?

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