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A function f(x) is said to have a jump discontinuity at x = a if:

1. \( \displaystyle{ \lim_{x\to a^-}f(x)}\) exists.

2. \( \displaystyle{ \lim_{x\to a^+}f(x)}\) exists.

3. The left and right limits are not equal.

 

Let \(f(x) = \begin{cases} 5 x - 2, &\text{if}\ x<10\\ \frac{4}{x+5}, &\text{if}\ x\geq 10 \end{cases}\)

Show that f(x) has a jump discontinuity at x = 10 by calculating the limits from the left and right at x = 10.

\(\displaystyle{ \lim_{x\to 10^-}f(x)}=\) ?

\(\displaystyle{ \lim_{x\to 10^+}f(x)}=\) ?

 Feb 23, 2022
 #1
avatar+124595 
+1

Limit as f(x) approaches 10  from the left =   5(10) - 2 =   48

 

Limit as f(x) approaches 10 from  the right   =   4 / ( 10 + 5)  =  4 / 15

 

 

cool cool cool

 Feb 23, 2022

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