Prove that for any positive integer

MATHEMATICS · Subjective · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Prove that for any positive integer nn, the following limit holds: lim⁡h→0(x+h)n−xnh=n x n−1.\lim_{h\to 0}\frac{(x+h)^n-x^n}{h}=n\,x^{\,n-1}.

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