Name: Limits Worksheet With Worked Solutions
Brand: Superprof
SKU: SP-RB-00011830
Rating: 4 (2 reviews)

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Exercise 1

Using the definition of a limit, prove that:

$\text{[math]}$

Exercise 2

Using the graph of the function f(x), determine the following limits.

Exercise 3

Using the definition of a limit, prove that:

$\text{[math]}$ has a limit −1 as x 0

Calculate the Following Limits:

Exercise 4

$\text{[math]}$

Exercise 5

$\text{[math]}$

Exercise 6

$\text{[math]}$

Exercise 7

$\text{[math]}$

Solution of exercise 1

Using the definition of a limit, prove that:

$\text{[math]}$

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

If $\text{[math]}$

$\text{[math]}$

To check this, take a $\text{[math]}$ .

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

For $\text{[math]}$ .

Solution of exercise 2

Using the graph of the function f(x), determine the following limits.

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

Solution of exercise 3

Using the definition of a limit, prove that:

$\text{[math]}$ has a limit −1 as x 0

$\text{[math]}$

Left side limit.

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

Right side limit

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

Solution of exercise 4

Calculate the limit:

$\text{[math]}$

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

Calculate the side limits to determine the sign of $\text{[math]}$ .

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

No limit.

Solution of exercise 5

Calculate the limit:

$\text{[math]}$

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

Solution of exercise 6

Calculate the limit:

$\text{[math]}$

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

Solution of exercise 7

Calculate the limit:

$\text{[math]}$

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

Summarise with AI:

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Continuity on a Closed Interval

Essential Discontinuity

One-Sided Limit

Bolzano’s Theorem

Limits at Infinity

Infinite Limit

Limit of a Logarithmic Function

Removable Discontinuity

Limit of an Exponential Function

Limit Rules

The Properties of Infinity in Calculus

One to the Power of Infinity

Limits and Dividing by Zero: Theory and Examples

Understanding All the Indeterminate Forms

Zero Over Zero: Indeterminate Forms and L’Hôpital’s Rule

What Is Zero Times Infinity? Theory and Practice Problems

Infinity Minus Infinity: Worked Examples and Solutions

Extreme Value Theorem in Calculus

Intermediate Value Theorem: Theory and Worked Examples

Discontinuous Function Graph Examples And Problems

What is a Continuous Function?

Jump Discontinuity Example Questions With Full Solutions

Formulas

Continuity Formulas

Limit Formulas

Exercises

Limit Problems

Intermediate Value Theorem Problems

Continuity Worksheet

Continuity Practice Problems for A Level Maths

Limits Worksheet With Worked Solutions

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Deepak Singh Brar

June 2026

what will be sign of -infinity is to power infinity plus or minus

Vanessa - Editorial Manager Superprof UK

July 2026

The sign **cannot be determined**.

For a negative base:

* **Even exponent** → **positive**
* **Odd exponent** → **negative**

So as the exponent tends to infinity, the sign depends on whether the exponent is even or odd. Therefore, ((-\infty)^\infty) has **no definite sign**—it can be **positive or negative**.

Summarise with AI:

Chapters

Exercise 1
Exercise 2
Exercise 3
Calculate the Following Limits:
Exercise 4
Exercise 5
Exercise 6
Exercise 7
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