en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor (1+x)^5

Solution

taylor

(1 + x)^{5}

Solution

1 + 5 x + 10 x^{2} + 10 x^{3} + 5 x^{4}

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{5} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{5} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{5} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{5}{1 !} x + \frac{20}{2 !} x^{2} + \frac{60}{3 !} x^{3} + \frac{120}{4 !} x^{4}

Refine

= 1 + 5 x + 10 x^{2} + 10 x^{3} + 5 x^{4}

Popular Examples

integral from 0 to 9 of 1/((x-1)^{1/3)}

\int_{0}^{9} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

tangent of f(x)=x^3-2x^2-5x+6,\at x=2 tangent of

f (x) = x^{3} - 2 x^{2} - 5 x + 6, at x = 2

integral from 0 to 3 of 15sqrt(8x+1)

\int_{0}^{3} 15 8 x + 1 d x

integral of ge^{-ct}

\int g e^{- c t} d t

derivative of axsin(4x+bxcos(4x))

\frac{d}{d x} (a x sin (4 x) + b x cos (4 x))

Frequently Asked Questions (FAQ)

What is taylor (1+x)^5 ?
The answer to taylor (1+x)^5 is 1+5x+10x^2+10x^3+5x^4