A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# Evaluate the limit lim _{h → 0} (x + h)^{3} - x^{3} / h

**Solution:**

Limits in maths are defined as the values that a function approaches the output for the given input values.

Limits play a vital role in calculus and mathematical analysis and are used to define integrals, derivatives, and continuity.

It is used in the analysis process, and it always concerns the behavior of the function at a particular point.

lim _{h → 0} (x + h)^{3} - x^{3} / h

Expanding the __numerator__ we have:

lim _{h → 0} [x^{3} + h^{3} + 3x^{2}h + 3h^{2}x - x^{3}]/h

lim _{h → 0} [h^{3} + 3x^{2}h + 3h^{2}x]/h

Simplifying further we have:

lim _{h → 0} [h^{2} + 3x^{2} + 3hx]

lim _{h → 0} [h^{2} + 3x^{2} + 3hx] = 3x^{2}

## Evaluate the limit lim _{h → 0} (x + h)^{3} - x^{3} / h

**Summary:**

Evaluate the limit lim _{h → 0} (x + h)^{3} - x^{3} / h we get 3x^{2}

Math worksheets and

visual curriculum

visual curriculum