Mathematics

Problem

For

f(x)=x^{5}

, consider the expression

\dfrac{(x+h)^{5}-x^{5}}{h}

. Which of the following is the correct expansion of this expression after dividing by

h

but before taking the limit as

h\to0

? a)

5x^{4}h+10x^{3}h^{2}+10x^{2}h^{3}+5xh^{4}+h^{5}

5x^{4}+10x^{3}+10x^{2}h+5xh^{2}+h^{3}

5x^{4}+10x^{3}h+10x^{2}h^{2}+5xh^{3}+h^{4}

5x^{4}