Calculus Practice Questions and Solutions: Limits, Derivatives, and Integration

Calculus Made Easy


Calculus is the study of how things change. It helps us understand motion, growth, and areas under

curves. It has two main parts: Limits, Derivatives, and Integration. Let's understand each in simple

words.



1. Limits
Limits help us find out what value a function approaches as the input gets closer to a certain

number. Example: As x gets closer to 2, what does x^2 get closer to? Answer: 4. Limits are

important to understand how functions behave.


Example 1:

Find the limit: lim (x -> 3) (x^2)

Solution: Put x = 3, we get 3^2 = 9. So, the limit is 9.



2. Derivatives
Derivatives show how fast something is changing. It's like finding the speed of a moving car at a

certain moment. It is the slope (steepness) of a curve at a point.


Example 2:

Find the derivative of y = x^2.

Solution: The rule says bring down the power and subtract 1.

So, derivative of x^2 is 2x.


Example 3:

Find the derivative of y = 3x^3.

Solution: Derivative of 3x^3 is 9x^2.