en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor (x-5)^{7/3}

Solution

taylor

(x - 5)^{\frac{7}{3}}

Solution

25 (- 1)^{\frac{1}{3}} \cdot 5^{\frac{1}{3}} - \frac{35 ( - 1 ) ^{\frac{1}{3}} \cdot 5 ^{\frac{1}{3}}}{3} x + \frac{14 ( - 1 ) ^{\frac{1}{3}} \cdot 5 ^{\frac{1}{3}}}{9} x^{2} + \frac{14}{81 ( - 1 ) ^{\frac{2}{3}} \cdot 5 ^{\frac{2}{3}}} x^{3} + \frac{7}{1215 ( - 1 ) ^{\frac{2}{3}} \cdot 5 ^{\frac{2}{3}}} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 25 (- 1)^{\frac{1}{3}} \cdot 5^{\frac{1}{3}} + \frac{\frac{d}{d x} ( ( x - 5 ) ^{\frac{7}{3}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( x - 5 ) ^{\frac{7}{3}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( x - 5 ) ^{\frac{7}{3}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 25 (- 1)^{\frac{1}{3}} \cdot 5^{\frac{1}{3}} + \frac{- \frac{35 ( - 1 ) ^{\frac{1}{3}} \cdot 5 ^{\frac{1}{3}}}{3}}{1 !} x + \frac{\frac{28 ( - 1 ) ^{\frac{1}{3}} \cdot 5 ^{\frac{1}{3}}}{9}}{2 !} x^{2} + \frac{\frac{28}{27 ( - 1 ) ^{\frac{2}{3}} \cdot 5 ^{\frac{2}{3}}}}{3 !} x^{3} + \frac{\frac{56}{405 ( - 1 ) ^{\frac{2}{3}} \cdot 5 ^{\frac{2}{3}}}}{4 !} x^{4} + \dots

Refine

= 25 (- 1)^{\frac{1}{3}} \cdot 5^{\frac{1}{3}} - \frac{35 ( - 1 ) ^{\frac{1}{3}} \cdot 5 ^{\frac{1}{3}}}{3} x + \frac{14 ( - 1 ) ^{\frac{1}{3}} \cdot 5 ^{\frac{1}{3}}}{9} x^{2} + \frac{14}{81 ( - 1 ) ^{\frac{2}{3}} \cdot 5 ^{\frac{2}{3}}} x^{3} + \frac{7}{1215 ( - 1 ) ^{\frac{2}{3}} \cdot 5 ^{\frac{2}{3}}} x^{4} + \dots

Popular Examples

limit as x approaches 3 of 2/((x-3))

x \to 3 lim (\frac{2}{( x - 3 )})

slope of x^2+4x-1 slope

x^{2} + 4 x - 1

(\partial)/(\partial x)(2xy+5y^2-3xy^3)

\frac{\partial}{\partial x} (2 x y + 5 y^{2} - 3 x y^{3})

limit as x approaches 1 of e^{5x^4-5x}

x \to 1 lim (e^{5 x^{4} - 5 x})

(\partial)/(\partial x)(x^3y+z^2x-zy^2)

\frac{\partial}{\partial x} (x^{3} y + z^{2} x - z y^{2})

Frequently Asked Questions (FAQ)

What is taylor (x-5)^{7/3} ?
The answer to taylor (x-5)^{7/3} is