When simplifying the expression

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

\dfrac{(x+h)^3-x^3}{h}

, terms containing

h^2

and

h^3

do not influence the value of the limit as

h\to0

. Explain why these higher–power terms can be ignored in determining the final limit.

Related theory

Limits
Derivative Foundations
Differentiation from first principles
Derivatives
Limits and Derivatives

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