Analyze the continuity of the function below. Determine the type(s) of discontin

Haven

Haven

Answered question

2021-11-05

Analyze the continuity of the function below. Determine the type(s) of discontinuity and justify your answer.
f(x)={x,ifx<03,ifx=0x2,if0<x<3x+6,ifx3

Answer & Explanation

wheezym

wheezym

Skilled2021-11-06Added 103 answers

To determine types of dicontinuity and justify your answer:
f(x)={x,ifx<03,ifx=0x2,if0<x<3x+6,ifx3
When x=0
limx0f(x)=limx0x=0
limx0+f(x)=limx0+x2=0
f(0)=3
limx0f(x)f(0)
f(x) is not continuous at x=0
when x=3
limx3f(x)=limx3x2=9
limx3+f(x)=limx3+x+6=9
f(3)=3+6=9
limx3f(x)=f(3)
f(x) is continuous at x=3
Therefore, f(x) is not continuous only at x=0

Jeffrey Jordon

Jeffrey Jordon

Expert2022-06-28Added 2605 answers

Answer is given below (on video)

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