Chapters

Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Solution of exercise 1
Solution of exercise 2
Solution of exercise 3
Solution of exercise 4
Solution of exercise 5
Solution of exercise 6
Solution of exercise 7
Solution of exercise 8
Solution of exercise 9

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Exercise 1

Find the point(s) of discontinuity for the function $\text{[math]}$ .

Exercise 2

Consider the function:

$\text{[math]}$

If $\text{[math]}$ , determine the values of a and b for which f(x) is continuous.

Exercise 3

Given the function:

$\text{[math]}$

Determine the value of a for which the function is continuous at $\text{[math]}$ .

Exercise 4

Given the function:

$\text{[math]}$

Determine the points of discontinuity.

Exercise 5

Given the function:

$\text{[math]}$

Determine a and b so that the function $\text{[math]}$ is continuous for all values of x.

Exercise 6

Given the function:

$\text{[math]}$

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

Exercise 7

Calculate the value of k for the following continuous function.

$\text{[math]}$

Exercise 8

Given the function:

$\text{[math]}$

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.

$\text{[math]}$

Solution of exercise 1

Find the point(s) of discontinuity for the function $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

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

Solution of exercise 2

Consider the function:

$\text{[math]}$

If $\text{[math]}$ , determine the values of a and b for which f(x) is continuous.

There is only a question of continuity at $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

For the function to be continuous:

$\text{[math]}$

On the other hand there is:

$\text{[math]}$

Solve the system of equations and obtain:

$\text{[math]}$

Solution of exercise 3

Given the function:

$\text{[math]}$

Determine the value of a for which the function is continuous at $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 4

Given the function:

$\text{[math]}$

Determine the points of discontinuity.

The exponential function is positive for all $\text{[math]}$ , therefore the denominator of the function cannot be annulled.

There is only doubt of the continuity at $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$

Solve the indeterminate form dividing by $\text{[math]}$

$\text{[math]}$

The function is continuous on $\text{[math]}$ .

Solution of exercise 5

Given the function:

$\text{[math]}$

Determine a and b so that the function $\text{[math]}$ is continuous for all values of x.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 6

Given the function:

$\text{[math]}$

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

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 7

Calculate the value of k for the following continuous function.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Therefore there is no limit for the function and there is no value that would make f(x) continuous at $\text{[math]}$ , regardless of what value k is given.

Solution of exercise 8

Given the function:

$\text{[math]}$

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

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

Solution of exercise 9

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

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

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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.

Theory

Continuity on a Closed Interval

Limit of a Logarithmic Function

Limit of an Exponential Function

Formulas

Exercises

Intermediate Value Theorem Problems

Cancel reply

Laura

February 2024

Correct equals infinity equals 16 but not true. It’s it’s six it’s infinity.

Cqndrm

April 2024

∞ = -1/12
By Sriniwas aramanujan

TonyL

September 2023

And this, my friends, is why humans will be conquered by AI… so many logic holes it’s… well, infinite. lol

Raj

May 2023

Is 0^infinity ( zero to the power infinity) indeterminate form? How?

Tara Kapali

May 2023

Didn’t Cantor proved that there are a group of infinities (the Aleph zero & Aleph one sets, for example)? And these are grouped around the concept of infinite to the power infinity, if I remember correctly .

Dhayq

July 2022

Exercise 3
I think it is discontinuous at 0

rohit

September 2020

exercise 2 : the function is not defined for x= 0.

rohit

September 2020

exercise 1 q 5 The function has a jump discontinuity at x = 1, should be x=0.

Continuity Problems

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Solution of exercise 6

Solution of exercise 7

Solution of exercise 8

Solution of exercise 9

Theory

One to the Power of Infinity

Zero Over Zero

Calculating Limits

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Continuity on a Closed Interval

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Division by Zero

Essential Discontinuity

Intermediate Value Theorem

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Zero Times Infinity

Infinity Minus Infinity

Infinity over Infinity

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Limit of a Logarithmic Function

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Limit of an Exponential Function

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