What is taylor x^5,x=2 ?

The answer to taylor x^5,x=2 is 32+80(x-2)+80(x-2)^2+40(x-2)^3+10(x-2)^4

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taylor x^5,x=2

taylor

x^{5}, x = 2

32 + 80 (x - 2) + 80 (x - 2)^{2} + 40 (x - 2)^{3} + 10 (x - 2)^{4}

Solution steps

Apply the Taylor Formula

= 32 + \frac{\frac{d}{d x} ( x ^{5} ) ( 2 )}{1 !} (x - 2) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{5} ) ( 2 )}{2 !} (x - 2)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{5} ) ( 2 )}{3 !} (x - 2)^{3} + \dots

Evaluate Derivatives

= 32 + \frac{80}{1 !} (x - 2) + \frac{160}{2 !} (x - 2)^{2} + \frac{240}{3 !} (x - 2)^{3} + \frac{240}{4 !} (x - 2)^{4}

Refine

= 32 + 80 (x - 2) + 80 (x - 2)^{2} + 40 (x - 2)^{3} + 10 (x - 2)^{4}

y = x^{2} + 3 x + 11

\frac{3}{1 + 3 x}

\int x 5 + 2 x d x

\frac{d}{d x} (2 sin (x) - cos (2 x))

y^{^{''}} - 4 y^{^{'}} + 3 y = 10 e^{3 t}

What is taylor x^5,x=2 ?
The answer to taylor x^5,x=2 is 32+80(x-2)+80(x-2)^2+40(x-2)^3+10(x-2)^4