Evaluate the limit lim _{h → 0} (x + h)³ - x³ / 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 - x³ / h

Expanding the numerator we have:

lim _{h → 0} [x³ + h³ + 3x²h + 3h²x - x³]/h

lim _{h → 0} [h³ + 3x²h + 3h²x]/h

Simplifying further we have:

lim _{h → 0} [h² + 3x² + 3hx]

lim _{h → 0} [h² + 3x² + 3hx] = 3x²

Evaluate the limit lim _{h → 0} (x + h)³ - x³ / h

Summary:

Evaluate the limit lim _{h → 0} (x + h)³ - x³ / h we get 3x²