# Continuity Problems

### Solutions

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

## 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