en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

taylor

Solution

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

Popular Examples

integral from 1 to 3 of (3-x)^2

integral of 4x^3+2xy^2ln(x^2+y^2)

(x^2-xy)dx+xdy=0

integral of (x+1)/(x-2)

sum from n=0 to infinity of 7/(5^n)

Frequently Asked Questions (FAQ)

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