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For the following exercise,

With the use of a graphing utility, use numerical or graphical evidence to determine the left- and right-hand limits of the function given as xx approaches aa. If the function has limit as xx approaches aa, state it. If not, discuss why there is no limit.

f(x)={x1, if x1x3, if x=1a=1f(x)=\left\{\begin{array}{ll}|x|-1, & \text { if } x \neq 1 \\ x^3, & \text { if } x=1\end{array} \quad a=1\right.


Answered 2 years ago
Answered 2 years ago
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In order to solve this, first, we need to check what we get for

limx1f(x).\lim_{x\to 1^-}f(x).

We can see from the graph below that as we take values of xx sufficiently close to 11, such that x<1x<1 and x1x\neq1, the output values approach to 00.

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