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Popular >

taylor x^{9/6},8

Solution

taylor

x^{\frac{9}{6}}, 8

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

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\int \frac{4}{5} - \frac{9}{x} d x

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\frac{d}{d x} (0.01 x^{3})

tangent of sqrt(2x^2+x-7)tangent of

2 x^{2} + x - 7

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