What is taylor 1/(x+4),0 ?

The answer to taylor 1/(x+4),0 is 1/4-1/16 x+1/64 x^2-1/256 x^3+1/1024 x^4+\ldots

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taylor 1/(x+4),0

taylor

\frac{1}{x + 4}, 0

\frac{1}{4} - \frac{1}{16} x + \frac{1}{64} x^{2} - \frac{1}{256} x^{3} + \frac{1}{1024} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{4} + \frac{\frac{d}{d x} ( \frac{1}{x + 4} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x + 4} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x + 4} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{4} + \frac{- \frac{1}{16}}{1 !} x + \frac{\frac{1}{32}}{2 !} x^{2} + \frac{- \frac{3}{128}}{3 !} x^{3} + \frac{\frac{3}{128}}{4 !} x^{4} + \dots

Refine

= \frac{1}{4} - \frac{1}{16} x + \frac{1}{64} x^{2} - \frac{1}{256} x^{3} + \frac{1}{1024} x^{4} + \dots

What is taylor 1/(x+4),0 ?
The answer to taylor 1/(x+4),0 is 1/4-1/16 x+1/64 x^2-1/256 x^3+1/1024 x^4+\ldots