# Calculus Examples

Consider the limit definition of the derivative.

Evaluate the function at .

Replace the variable with in the expression.

Simplify the result.

Apply the distributive property.

The final answer is .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Group the last three terms.

Factor.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Remove unnecessary parentheses.

Multiply by .

Remove unnecessary parentheses.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Apply the distributive property.

Multiply by .

Remove unnecessary parentheses.

Subtract from .

Add and .

Subtract from .

Add and .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Evaluate the limit of which is constant as approaches .