CPM Homework Help : CALC Problem 4-75

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4-75.

The graph of a function $f(x)$ is given at right. Use the graph to evaluate the following limits.

$\lim\limits_ { x \rightarrow - 1 } f ( x )$
Answer (a):
The limit does not exist, but $y→+∞$ .

$\lim\limits_ { x \rightarrow 2 } f ( x )$
Hint (b):
A limit is a predicted value (which sometimes differs from the actual function value). The prediction must agree from the left and the right.

$\lim\limits_ { x \rightarrow 2 ^ { - } } f ( x )$
Hint (c):
What is the prediction from the left?

$\lim\limits_ { x \rightarrow 2 ^ { + } } f ( x )$
Hint (d):
What is the prediction from the right?

$\lim\limits_ { x \rightarrow 5 } f ( x )$
Hint (e):
Most of the time, the limit and the function value agree.

$\lim\limits_ { x \rightarrow \infty } f ( x )$
Hint (f):
$\operatorname{lim }x→∞$ and $\operatorname{lim }x→−∞$ will reveal the equation of a horizontal asymptote, if there is one.

Where (if anywhere) does the derivative of $f(x)$ not exist?
Hint (g):
Look for cusps, endpoints, jumps, holes, and vertical asymptotes.

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