What is taylor x^4,1 ?

The answer to taylor x^4,1 is 1+4(x-1)+6(x-1)^2+4(x-1)^3+(x-1)^4

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taylor x^4,1

taylor

x^{4}, 1

1 + 4 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( x ^{4} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{4} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{4} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{4}{1 !} (x - 1) + \frac{12}{2 !} (x - 1)^{2} + \frac{24}{3 !} (x - 1)^{3} + \frac{24}{4 !} (x - 1)^{4}

Refine

= 1 + 4 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

- \frac{2 x}{x ^{2} + 1}

\int_{0}^{l n (2)} s e^{s} d s

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

x \to - 2 lim (- x^{2} + 4 x - 6)

f (x) = x^{2} + 1, (- 2, 5)

What is taylor x^4,1 ?
The answer to taylor x^4,1 is 1+4(x-1)+6(x-1)^2+4(x-1)^3+(x-1)^4