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

The answer to taylor 1/(x^2),2 is 1/4-1/4 (x-2)+3/16 (x-2)^2-1/8 (x-2)^3+5/64 (x-2)^4+\ldots

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taylor 1/(x^2),2

taylor

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

\frac{1}{4} - \frac{1}{4} (x - 2) + \frac{3}{16} (x - 2)^{2} - \frac{1}{8} (x - 2)^{3} + \frac{5}{64} (x - 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{4} + \frac{- \frac{1}{4}}{1 !} (x - 2) + \frac{\frac{3}{8}}{2 !} (x - 2)^{2} + \frac{- \frac{3}{4}}{3 !} (x - 2)^{3} + \frac{\frac{15}{8}}{4 !} (x - 2)^{4} + \dots

Refine

= \frac{1}{4} - \frac{1}{4} (x - 2) + \frac{3}{16} (x - 2)^{2} - \frac{1}{8} (x - 2)^{3} + \frac{5}{64} (x - 2)^{4} + \dots

(2 x^{2} y + 2 1 + x^{4} y^{2}) d x + x^{3} d y = 0

\frac{d}{d x} ((4 x + 3)^{4} (x + 1)^{- 3})

\frac{d q}{d t} + \frac{1}{5 \cdot 1 0 ^{- 9}} q = \frac{200}{1000}

\int \frac{( ln ^{6} ( x ) )}{x} d x

\frac{d}{d x} (e^{(x + y)} - 1)

What is taylor 1/(x^2),2 ?
The answer to taylor 1/(x^2),2 is 1/4-1/4 (x-2)+3/16 (x-2)^2-1/8 (x-2)^3+5/64 (x-2)^4+\ldots