+0

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

-1
145
1
+73

Show that

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

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
+124595
+1

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

Feb 23, 2022