What is taylor x^5,1 ?

The answer to taylor x^5,1 is 1+5(x-1)+10(x-1)^2+10(x-1)^3+5(x-1)^4

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taylor x^5,1

taylor

x^{5}, 1

1 + 5 (x - 1) + 10 (x - 1)^{2} + 10 (x - 1)^{3} + 5 (x - 1)^{4}

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( x ^{5} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{5} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{5} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{5}{1 !} (x - 1) + \frac{20}{2 !} (x - 1)^{2} + \frac{60}{3 !} (x - 1)^{3} + \frac{120}{4 !} (x - 1)^{4}

Refine

= 1 + 5 (x - 1) + 10 (x - 1)^{2} + 10 (x - 1)^{3} + 5 (x - 1)^{4}

\frac{\partial}{\partial y} (2 x^{2} y^{2})

t \to - \infty lim (- \frac{1}{3} + \frac{1}{3} e^{- t^{3}})

y^{^{''}} - 9 y^{^{'}} + 9 y = 0

n = 1 \sum \infty \frac{2}{n + 7}

What is taylor x^5,1 ?
The answer to taylor x^5,1 is 1+5(x-1)+10(x-1)^2+10(x-1)^3+5(x-1)^4