Question: The Binomial Theorem states that for any positive integer n, Use this formula and the definition to show that d/dx (x n ) = nx

The Binomial Theorem states that for any positive integer n,

п(n — 1) (a + b)


Use this formula and the definition

f(x + h) – f(x) f' (x) = lim


to show that d/dx (xn) = nxn - 1, for any positive integer n.

(n 1) (a + b)" = a" + na"-'b + 21 a"-22 ( 1)( 2) 3.2.1 a"-'b3 + . + nab"-! + b". "- f(x + h) f(x) f' (x) = lim

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