# Continuity Problems

### Solutions

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

2Consider the function:

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

3Given the function:

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

4Given the function:

Determine the points of discontinuity.

5Given the function:

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

6Given the function:

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

7Calculate the value of **k** for the following continuous function.

8Given the function:

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

9Determine the values for **a** and **b** in order to create a continuous function.

## 1

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

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

## 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

## 3

Given the function:

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

## 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.

## 5

Given the function:

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

## 6

Given the function:

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

## 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.

## 8

Given the function:

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

## 9

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

b= 1

3a = −2 a = −1