For , consider the expression . Which of the following is the correct expansion of…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For f(x)=x5f(x)=x^{5}, consider the expression (x+h)5−x5h\dfrac{(x+h)^{5}-x^{5}}{h}. Which of the following is the correct expansion of this expression after dividing by hh but before taking the limit as h→0h\to0? (a) 5x4h+10x3h2+10x2h3+5xh4+h55x^{4}h+10x^{3}h^{2}+10x^{2}h^{3}+5xh^{4}+h^{5} (b) 5x4+10x3+10x2h+5xh2+h35x^{4}+10x^{3}+10x^{2}h+5xh^{2}+h^{3} (c) 5x4+10x3h+10x2h2+5xh3+h45x^{4}+10x^{3}h+10x^{2}h^{2}+5xh^{3}+h^{4} (d) 5x45x^{4}

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