What is taylor 1/(x+4),2 ?

The answer to taylor 1/(x+4),2 is 1/6-1/36 (x-2)+1/216 (x-2)^2-1/1296 (x-2)^3+1/7776 (x-2)^4+\ldots

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taylor 1/(x+4),2

taylor

\frac{1}{x + 4}, 2

\frac{1}{6} - \frac{1}{36} (x - 2) + \frac{1}{216} (x - 2)^{2} - \frac{1}{1296} (x - 2)^{3} + \frac{1}{7776} (x - 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{6} + \frac{\frac{d}{d x} ( \frac{1}{x + 4} ) ( 2 )}{1 !} (x - 2) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x + 4} ) ( 2 )}{2 !} (x - 2)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x + 4} ) ( 2 )}{3 !} (x - 2)^{3} + \dots

Evaluate Derivatives

= \frac{1}{6} + \frac{- \frac{1}{36}}{1 !} (x - 2) + \frac{\frac{1}{108}}{2 !} (x - 2)^{2} + \frac{- \frac{1}{216}}{3 !} (x - 2)^{3} + \frac{\frac{1}{324}}{4 !} (x - 2)^{4} + \dots

Refine

= \frac{1}{6} - \frac{1}{36} (x - 2) + \frac{1}{216} (x - 2)^{2} - \frac{1}{1296} (x - 2)^{3} + \frac{1}{7776} (x - 2)^{4} + \dots

3 e^{\frac{1}{x}}

\int_{0}^{π} sin^{2} (8 x) d x

\int_{- 4}^{4} (3 - x) d x

x \to 0 lim ((sin (x^{2}) + 1)^{\frac{1}{5 x ^{2}}})

\frac{d}{d x} (0.882 x^{0.842})

What is taylor 1/(x+4),2 ?
The answer to taylor 1/(x+4),2 is 1/6-1/36 (x-2)+1/216 (x-2)^2-1/1296 (x-2)^3+1/7776 (x-2)^4+\ldots