Continuity Problems
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}.
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
