CPM Homework Help : CALC Problem 3-95

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3-95.

Evaluate each limit. If the limit does not exist, say so but also state if $y$ is approaching positive or negative infinity.

$\lim\limits_ { x \rightarrow 0 } \frac { x ^ { 2 } + 3 x - 10 } { x - 2 }$
Hint (a):
This limit can be evaluated without any fancy Algebra steps.

$\lim\limits _ { x \rightarrow - 5 } \frac { x ^ { 2 } + 3 x - 10 } { x - 2 }$
Hint (b):
Refer to the hint in part (a). Limits like these suggest that the actual value $f(-5)$ and the limit $x→−5$ agree.

$\lim\limits _ { x \rightarrow 2 } \frac { x ^ { 2 } + 3 x - 10 } { x - 2 }$
Hint (c):
Factor first. Since the denominator $→ 0$ , we are investigating whether there is a hole or an asymptote.

$\lim\limits_ { x \rightarrow \infty } \frac { x ^ { 2 } + 3 x - 10 } { x - 2 }$
Hint (d):
This limit $→∞$ .Compare the highest-power term in the numerator and denominator. Does the graph have a horizontal asymptote or does it approach $∞$ or $−∞$ ?

Use the limits above to describe the shape of the graph of $y = \frac { x ^ { 2 } + 3 x - 10 } { x - 2 }$ . State all horizontal asymptotes, vertical asymptotes and holes.
Hint (e):
Refer to the Hints in parts (c) and (d).

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