Lesson: Continuity of a Function

In this lesson, we will learn how to determine the continuity of a function at a point on the number line by evaluating limits at that point.

Explainer

  • +2

Sample Question Videos

  • 03:59
  • 05:23
  • 02:40

Worksheet: Continuity of a Function • 25 Questions • 4 Videos

Q1:

Let Find the value of 𝑎 that makes 𝑓 continuous at 𝑥 = 9 .

Q2:

Find the set on which 𝑓 ( 𝑥 ) = 𝑥 + 1 4 + 3 𝑥 is continuous.

Q3:

Discuss the continuity of the function 𝑓 ( 𝑥 ) = 𝑥 1 𝑥 1 6 on .

Q4:

Find the value of 𝑘 which makes the function 𝑓 continuous at 𝑥 = 3 , given

Q5:

Discuss the continuity of the function 𝑓 at 𝑥 = 7 , given that

Q6:

Let What can be said of the continuity of 𝑓 at 𝑥 = 7 ?

Q7:

Find l i m 𝑥 9 𝑓 ( 𝑥 ) and l i m 𝑥 9 + 𝑓 ( 𝑥 ) , where

Q8:

Find the values of 𝑐 which make the function 𝑓 continuous at 𝑥 = 𝑐 if

Q9:

Find the set of values of 𝑥 for which the function given by 𝑓 ( 𝑥 ) = 5 𝑥 1 3 is continuous.

Q10:

Find the set on which 𝑓 ( 𝑥 ) = 𝑥 2 2 𝑥 2 𝑥 6 3 2 is continuous.

Q11:

Use continuity to evaluate l i m s i n s i n 𝑥 𝜋 6 ( 2 𝑥 7 6 𝑥 ) .

Q12:

Find the set on which 𝑓 ( 𝑥 ) = 𝑥 + 9 𝑥 + 1 c o s is continuous.

Q13:

Given that 𝑓 and 𝑔 are continuous functions such that 𝑔 ( 6 ) = 6 and l i m 𝑥 6 [ 𝑓 ( 𝑥 ) 9 𝑓 ( 𝑥 ) 𝑔 ( 𝑥 ) ] = 5 , determine 𝑓 ( 6 ) .

Q14:

Which of the following holds for 𝑓 ( 𝑥 ) = ( 7 𝑥 + 3 ) + 3 5 𝑥 7 s i n ?

Q15:

Use continuity to evaluate l i m 2 𝑥 2 2 + 3 𝑥 .

Q16:

Use continuity to evaluate l i m 𝑥 1 3 𝑥 + 2 𝑥 1 5 2 .

Q17:

Use continuity to evaluate l i m l n 𝑥 5 2 5 + 2 𝑥 6 𝑥 .

Q18:

Determine the value of 𝑎 that makes the function 𝑓 continuous at 𝑥 = 9 , given

Q19:

Suppose What can be said of the continuity of 𝑓 at 𝑥 = 0 ?

Q20:

Given 𝑓 ( 𝑥 ) = 𝑥 1 0 0 𝑥 1 0 , if possible or necessary, define 𝑓 ( 1 0 ) so that 𝑓 is continuous at 𝑥 = 1 0 .

Q21:

Suppose Discuss whether it is possible to define 𝑓 ( 6 ) to obtain a function that is continuous at this point.

Q22:

Determine whether the function represented by the graph is continuous or discontinuous.

Q23:

Given 𝑓 ( 𝑥 ) = 9 𝑥 + 𝑥 2 2 , what can be said of the continuity of 𝑓 at 𝑥 = 7 ?

Q24:

Find the set on which 𝑓 ( 𝑥 ) = 𝑥 + 5 ( 𝑥 + 8 ) s i n c o s is continuous.

Q25:

Discuss the continuity of the function 𝑓 ( 𝑥 ) = 3 𝑥 2 3 at 𝑥 = 6 .

Preview

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.