Chapter 1 - Limits and Their Properties - 1.4 Exercises: 49

$f(x)$ has an irremovable jump discontinuity at $x=-7.$

Work Step by Step

The function is 0/0, and not defined at $x=-7.$ $\lim\limits_{x\to-7^+}f(x)=\dfrac{|-7^++7|}{-7^++7}=\dfrac{0^+}{0^+}=1.$ $\lim\limits_{x\to-7^-}f(x)=\dfrac{|-7^-+7|}{-7^-+7}=\dfrac{0^+}{0^-}=-1.$ Since $\lim\limits_{x\to-7^+}f(x)\ne\lim\limits_{x\to-7^-}f(x)$ then $\lim\limits_{x\to7}f(x)$ doesn't exist. and the function has a jump discontinuity.

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