en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor (x+3)^{1/2}

Solution

taylor

(x + 3)^{\frac{1}{2}}

Solution

3^{\frac{1}{2}} + \frac{1}{2 \cdot 3 ^{\frac{1}{2}}} x - \frac{1}{24 \cdot 3 ^{\frac{1}{2}}} x^{2} + \frac{1}{144 \cdot 3 ^{\frac{1}{2}}} x^{3} - \frac{5}{3456 \cdot 3 ^{\frac{1}{2}}} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 3^{\frac{1}{2}} + \frac{\frac{1}{2 \cdot 3 ^{\frac{1}{2}}}}{1 !} x + \frac{- \frac{1}{12 \cdot 3 ^{\frac{1}{2}}}}{2 !} x^{2} + \frac{\frac{1}{24 \cdot 3 ^{\frac{1}{2}}}}{3 !} x^{3} + \frac{- \frac{5}{144 \cdot 3 ^{\frac{1}{2}}}}{4 !} x^{4} + \dots

Refine

= 3^{\frac{1}{2}} + \frac{1}{2 \cdot 3 ^{\frac{1}{2}}} x - \frac{1}{24 \cdot 3 ^{\frac{1}{2}}} x^{2} + \frac{1}{144 \cdot 3 ^{\frac{1}{2}}} x^{3} - \frac{5}{3456 \cdot 3 ^{\frac{1}{2}}} x^{4} + \dots

Popular Examples

integral of cos(z/y)

\int cos (\frac{z}{y}) d z

tangent of f(x)=-3x^2-2x^2-1,\at x=-1 tangent of

f (x) = - 3 x^{2} - 2 x^{2} - 1, at x = - 1

integral of (cos(x))/(5+sin(x))

\int \frac{cos ( x )}{5 + sin ( x )} d x

derivative of sqrt(11t^2+9)derivative of

11 t^{2} + 9

integral from 0 to 3 of 1/(x^2-6x+5)

\int_{0}^{3} \frac{1}{x ^{2} - 6 x + 5} d x

Frequently Asked Questions (FAQ)

What is taylor (x+3)^{1/2} ?
The answer to taylor (x+3)^{1/2} is