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Popular >

taylor X^{9/6},8,5

Solution

taylor

X^{\frac{9}{6}}, 8, 5

Solution

16 \cdot 2^{\frac{1}{2}} + 3 \cdot 2^{\frac{1}{2}} (X - 8) + \frac{3}{16 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{2} - \frac{1}{256 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{3} + \frac{3}{16384 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 16 \cdot 2^{\frac{1}{2}} + \frac{\frac{d}{d X} ( X ^{\frac{9}{6}} ) ( 8 )}{1 !} (X - 8) + \frac{\frac{d ^{2}}{d X ^{2}} ( X ^{\frac{9}{6}} ) ( 8 )}{2 !} (X - 8)^{2} + \frac{\frac{d ^{3}}{d X ^{3}} ( X ^{\frac{9}{6}} ) ( 8 )}{3 !} (X - 8)^{3} + \dots

Evaluate Derivatives

= 16 \cdot 2^{\frac{1}{2}} + \frac{3 \cdot 2 ^{\frac{1}{2}}}{1 !} (X - 8) + \frac{\frac{3}{8 \cdot 2 ^{\frac{1}{2}}}}{2 !} (X - 8)^{2} + \frac{- \frac{3}{128 \cdot 2 ^{\frac{1}{2}}}}{3 !} (X - 8)^{3} + \frac{\frac{9}{2048 \cdot 2 ^{\frac{1}{2}}}}{4 !} (X - 8)^{4} + \dots

Refine

= 16 \cdot 2^{\frac{1}{2}} + 3 \cdot 2^{\frac{1}{2}} (X - 8) + \frac{3}{16 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{2} - \frac{1}{256 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{3} + \frac{3}{16384 \cdot 2 ^{\frac{1}{2}}} (X - 8)^{4} + \dots

Popular Examples

integral of ((8x-3))/(x^2+x+1)

\int \frac{( 8 x - 3 )}{x ^{2} + x + 1} d x

sum from n=1 to infinity of 2^n-3

n = 1 \sum \infty 2^{n} - 3

derivative of 8^{x^3}

\frac{d}{d x} (8^{x^{3}})

(dy)/(dt)=4y+y^3

\frac{d y}{d t} = 4 y + y^{3}

integral of e^{nx}sin(nx)

\int e^{n x} sin (n x) d x

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