What is taylor e^{1/6 x^6},0 ?

The answer to taylor e^{1/6 x^6},0 is 1+1/6 x^6+\ldots

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taylor e^{1/6 x^6},0

taylor

e^{\frac{1}{6} x^{6}}, 0

1 + \frac{1}{6} x^{6} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{\frac{1}{6} x^{6}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{\frac{1}{6} x^{6}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{\frac{1}{6} x^{6}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{120}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 + \frac{1}{6} x^{6} + \dots

x \to - 6 - lim (- \frac{1}{x + 6})

\int_{1}^{3} (3 - x)^{2} d x

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

\int \frac{x + 1}{e ^{x}} d x

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

What is taylor e^{1/6 x^6},0 ?
The answer to taylor e^{1/6 x^6},0 is 1+1/6 x^6+\ldots