en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

maclaurin e^{-ix}

Solution

maclaurin

e^{- i x}

Solution

1 - i x - \frac{1}{2} x^{2} + \frac{i}{6} x^{3} + \frac{1}{24} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{- i}{1 !} x + \frac{- 1}{2 !} x^{2} + \frac{i}{3 !} x^{3} + \frac{1}{4 !} x^{4} + \dots

Refine

= 1 - i x - \frac{1}{2} x^{2} + \frac{i}{6} x^{3} + \frac{1}{24} x^{4} + \dots

Popular Examples

integral of 3/((3x-1)ln(3x-1))

\int \frac{3}{( 3 x - 1 ) ln ( 3 x - 1 )} d x

integral of sin^6(ax)

\int sin^{6} (a x) d x

integral of cos^2(v)

\int cos^{2} (v) d v

integral of (2x+15)e^{0.25x}

\int (2 x + 15) e^{0.25 x} d x

limit as x approaches infinity of 1^0

x \to \infty lim (1^{0})

Frequently Asked Questions (FAQ)

What is maclaurin e^{-ix} ?
The answer to maclaurin e^{-ix} is 1-ix-1/2 x^2+i/6 x^3+1/24 x^4+\ldots