Exercise 1

Find the point(s) of discontinuity for the function f(x) = x² + 1+ |2x − 1|.

Exercise 2

Consider the function:

If f (2) = 3, determine the values of a and b for which f(x) is continuous.

Exercise 3

Given the function:

Determine the value of a for which the function is continuous at x = 3.

Exercise 4

Given the function:

Determine the points of discontinuity.

Exercise 5

Given the function:

Determine a and b so that the function f(x) is continuous for all values of x.

Exercise 6

Given the function:

Determining the value of a for which f(x) is continuous.

Exercise 7

Calculate the value of k for the following continuous function.

Exercise 8

Given the function:

Determine the values for a and b in order to create a continuous function.

Exercise 9

Determine the values for a and b in order to create a continuous function.

Solution of exercise 1

Find the point(s) of discontinuity for the function f(x) = x² + 1+ |2x − 1|.

There are no points of discontinuity as the function is continuous.

Solution of exercise 2

Consider the function:

If f (2) = 3, determine the values of a and b for which f (x) is continuous.

There is only a question of continuity at x = 1.

For the function to be continuous:

On the other hand there is:

Solve the system of equations and obtain:

a = 1 b = −1

Solution of exercise 3

Given the function:

Determine the value of a for which the function is continuous at x = 3.

Solution of exercise 4

Given the function:

Determine the points of discontinuity for the function.

The exponential function is positive for all x , therefore the denominator of the function cannot be annulled.

There is only doubt of the continuity at x = 0.

Solve the indeterminate form dividing by

The function is continuous on − {0}.

See also in trigonometric working demo.

Solution of exercise 5

Given the function:

Determine a and b so that the function f(x) is continuous for all values of x.

Solution of exercise 6

Given the function:

Determining the value of a for which f(x) is continuous.

Solution of exercise 7

Calculate the value of k for the following continuous function.

Therefore there is no limit for the function and there is no value that would make f(x) continuous at x = 0, regardless of what value k is given.

Solution of exercise 8

Given the function:

Determine the values for a and b in order to create a continuous function.

Solution of exercise 9

Determine the values for a and b in order to create a continuous function.

b= 1

3a = −2 a = −1

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.