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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 a limit as xx approaches aa, state it. If not, discuss why there is no limit.

f(x)={1x3, if x2x3+1, if x>2a=2f(x)=\left\{\begin{array}{ll}\frac{1}{x}-3, & \text { if } x \leq 2 \\ x^3+1, & \text { if } x>2\end{array} a=2\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

limx2f(x).\lim_{x\to 2^-}f(x).

We can see from the graph below that as we take values of xx sufficiently close to 22, such that x<2x<2 and x2x\neq2, the output values approach to 2.5-2.5.

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