  ### Home > CALC > Chapter 4 > Lesson 4.2.3 > Problem4-75

4-75.

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

1. $\lim\limits_ { x \rightarrow - 1 } f ( x )$

The limit does not exist, but $y→+∞$.

1. $\lim\limits_ { x \rightarrow 2 } f ( x )$

A limit is a predicted value (which sometimes differs from the actual function value). The prediction must agree from the left and the right.

1. $\lim\limits_ { x \rightarrow 2 ^ { - } } f ( x )$

What is the prediction from the left?

1. $\lim\limits_ { x \rightarrow 2 ^ { + } } f ( x )$

What is the prediction from the right?

1. $\lim\limits_ { x \rightarrow 5 } f ( x )$

Most of the time, the limit and the function value agree.

1. $\lim\limits_ { x \rightarrow \infty } f ( x )$

$\operatorname{lim }x→∞$ and $\operatorname{lim }x→−∞$ will reveal the equation of a horizontal asymptote, if there is one.

1. Where (if anywhere) does the derivative of $f(x)$ not exist?

Look for cusps, endpoints, jumps, holes, and vertical asymptotes. 