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

Q1:

Discuss the continuity of the function π at π₯ = β 2 , given

Q2:

Given If possible or necessary, define π ( β 8 ) so that π is continuous at π₯ = β 8 .

Q3:

Suppose What can be said of the continuity of π at π₯ = β 1 ?

Q4:

Find the values of π and π that make the function π continuous at π₯ = β 1 and π₯ = β 6 , given that

Q5:

Given π ( π₯ ) = π₯ + π₯ β 2 π₯ β 1 ο¨ , if possible or necessary, define π ( 1 ) so that π is continuous at π₯ = 1 .

Q6:

Given π ( π₯ ) = π₯ β 6 4 π₯ + π₯ β 2 0 ο© ο¨ , if possible or necessary, define π ( 4 ) so that π is continuous at π₯ = 4 .

Q7:

Discuss the continuity of the function π at π₯ = 5 given

Q8:

Find the value of π that makes π continuous at π₯ = 3 , given that

Q9:

Setting π ( π ) = 5 4 and π ( π₯ ) = π₯ β π π₯ β π 6 6 3 3 when π₯ β π makes π continuous at π₯ = π . Determine π .

Q10:

Consider the function

What is π ( 0 ) ?

What is l i m π₯ β 0 β π ( π₯ ) ?

What is l i m π₯ β 0 + π ( π₯ ) ?

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

Q11:

Q12:

Determine the value of π that makes π continuous at π₯ = 0 , given

Q13:

Discuss the continuity of the function π at π₯ = 0 , given

Q14:

The function is continuous at π₯ = 0 . Determine the possible values of π .

Q15:

Determine the value of π that makes the function π continuous at π₯ = π 4 , given

Q16:

Find the value of π that makes the function π continuous at π₯ = π 4 , given that

Q17:

Discuss the continuity of the function π at π₯ = π 2 , given

Q18:

Determine the value of π that makes the function π continuous at π₯ = 0 , given that

Q19:

Find the value of π which makes the function π continuous at π₯ = 0 , given that

Q20:

Q21:

Let Find all values of that make continuous at .

Q22:

Let Find all values of π that make π continuous at π₯ = 0 .

Q23:

Suppose What can be said of the continuity of π at π₯ = 0 ?

Q24:

Find the value of π which makes the function π continuous at π₯ = 4 , given

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