What is taylor 1/(x^2)4 ?

The answer to taylor 1/(x^2)4 is 4-8(x-1)+12(x-1)^2-16(x-1)^3+20(x-1)^4+\ldots

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taylor 1/(x^2)4

taylor

\frac{1}{x ^{2}} 4

4 - 8 (x - 1) + 12 (x - 1)^{2} - 16 (x - 1)^{3} + 20 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 4 + \frac{- 8}{1 !} (x - 1) + \frac{24}{2 !} (x - 1)^{2} + \frac{- 96}{3 !} (x - 1)^{3} + \frac{480}{4 !} (x - 1)^{4} + \dots

Refine

= 4 - 8 (x - 1) + 12 (x - 1)^{2} - 16 (x - 1)^{3} + 20 (x - 1)^{4} + \dots

\frac{\partial}{\partial x} (\frac{6 x - 8 y}{6 x + 8 y})

\frac{\partial}{\partial y} ((x^{2} + y^{2})^{\frac{1}{2}})

f (x) = x^{2} - 4

\int \frac{1}{x ^{2} ( x + 1 ) ^{2}} d x

x - 2

What is taylor 1/(x^2)4 ?
The answer to taylor 1/(x^2)4 is 4-8(x-1)+12(x-1)^2-16(x-1)^3+20(x-1)^4+\ldots