What is taylor 2/x ,4 ?

The answer to taylor 2/x ,4 is 1/2-1/8 (x-4)+1/32 (x-4)^2-1/128 (x-4)^3+1/512 (x-4)^4+\ldots

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taylor 2/x ,4

taylor

\frac{2}{x}, 4

\frac{1}{2} - \frac{1}{8} (x - 4) + \frac{1}{32} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{1}{512} (x - 4)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= \frac{1}{2} - \frac{1}{8} (x - 4) + \frac{1}{32} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{1}{512} (x - 4)^{4} + \dots

y = 4 x^{2}, y = 6 x^{2}, 5 x + y = 6 \geq 0

\int e^{3 x + 8} d x

\frac{d}{d x} (\frac{cot ( x )}{1 + csc ( x )})

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

What is taylor 2/x ,4 ?
The answer to taylor 2/x ,4 is 1/2-1/8 (x-4)+1/32 (x-4)^2-1/128 (x-4)^3+1/512 (x-4)^4+\ldots