Lesson: Classifying Discontinuities Mathematics • Higher Education

In this lesson, we will learn how to differentiate between the three types of function discontinuity at a given point.

Lesson Video

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17:26

Sample Question Videos

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Lesson Worksheet

Q1:

Consider the function 𝑓(π‘₯)=1βˆ’π‘₯π‘₯<0,0π‘₯=0,1+2π‘₯π‘₯>0.whenwhenwhen

What is 𝑓(0)?

What is limο—β†’οŠ¦οŽͺ𝑓(π‘₯)?

What is limο—β†’οŠ¦οŽ©π‘“(π‘₯)?

What type of discontinuity does the function 𝑓 have at π‘₯=0?

Q2:

Consider the function 𝑓(π‘₯)=⎧βŽͺ⎨βŽͺβŽ©ο€Ό1π‘₯,π‘₯<0,0,π‘₯=0,1π‘₯,π‘₯>0.sinwhenwhenwhen

What is 𝑓(0)?

What is limο—β†’οŠ¦οŽͺ𝑓(π‘₯)?

What is limο—β†’οŠ¦οŽ©π‘“(π‘₯)?

What type of discontinuity does the function 𝑓 have at π‘₯=0?

Q3:

Consider the function 𝑓(π‘₯)=π‘₯+π‘₯π‘₯sincoscot. Find the type of discontinuity that the function 𝑓 has at π‘₯=πœ‹, if it has any.

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