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Popular >

taylor (-3x+14)^{4/3}

Solution

taylor

(- 3 x + 14)^{\frac{4}{3}}

Solution

14 \cdot 1 4^{\frac{1}{3}} - 4 \cdot 1 4^{\frac{1}{3}} x + (\frac{2}{49})^{\frac{1}{3}} x^{2} + \frac{2 ^{\frac{1}{3}}}{21 \cdot 7 ^{\frac{2}{3}}} x^{3} + \frac{5}{588 \cdot 1 4 ^{\frac{2}{3}}} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 14 \cdot 1 4^{\frac{1}{3}} + \frac{\frac{d}{d x} ( ( - 3 x + 14 ) ^{\frac{4}{3}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( - 3 x + 14 ) ^{\frac{4}{3}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( - 3 x + 14 ) ^{\frac{4}{3}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 14 \cdot 1 4^{\frac{1}{3}} + \frac{- 4 \cdot 1 4 ^{\frac{1}{3}}}{1 !} x + \frac{\frac{2 \cdot 2 ^{\frac{1}{3}}}{7 ^{\frac{2}{3}}}}{2 !} x^{2} + \frac{\frac{2 \cdot 2 ^{\frac{1}{3}}}{7 \cdot 7 ^{\frac{2}{3}}}}{3 !} x^{3} + \frac{\frac{5 \cdot 2 ^{\frac{1}{3}}}{49 \cdot 7 ^{\frac{2}{3}}}}{4 !} x^{4} + \dots

Refine

= 14 \cdot 1 4^{\frac{1}{3}} - 4 \cdot 1 4^{\frac{1}{3}} x + (\frac{2}{49})^{\frac{1}{3}} x^{2} + \frac{2 ^{\frac{1}{3}}}{21 \cdot 7 ^{\frac{2}{3}}} x^{3} + \frac{5}{588 \cdot 1 4 ^{\frac{2}{3}}} x^{4} + \dots

Popular Examples

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\int (x^{2} y - ln (cos (x))) d y

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

\int \frac{1}{x 2 x - 1} d x

derivative of y=x(x-10)derivative of

y = x (x - 10)

tangent of y=x^4+2e^x(0.2)tangent of

y = x^{4} + 2 e^{x} (0.2)

integral from 0 to 1 of sqrt(1-x^2)

\int_{0}^{1} 1 - x^{2} d x

Frequently Asked Questions (FAQ)

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