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\(f(x) = \begin{cases}\displaystyle{7x-4}&\text{if}\ x < 7\cr \displaystyle{\frac{5}{x+8}}&\text{if}\ x \ge 7\end{cases}\)

 

 

has a jump discontinuity at 7 by calculating the limit as x approaches 7 from the left and from the right.

 

\(\displaystyle{\lim_{x\to 7^-}f(x)} =\)

 

\(\displaystyle{\lim_{x\to 7^+}f(x)} =\)

 Feb 23, 2022
 #1
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lim f(x)                                            =      45

x approaches 7 from the left

 

lim f(x)                                            =      1/3 

x approaches 7 from  the right

 

The limits are not the same....so..we have a discontinuity as  x approaches 7 from  both  sides

 

cool cool cool

 Feb 23, 2022

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