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Popular Calculus >

taylor x^{9/6},2

Solution

taylor

x^{\frac{9}{6}}, 2

Solution

2 \cdot 2^{\frac{1}{2}} + \frac{3}{2 ^{\frac{1}{2}}} (x - 2) + \frac{3}{8 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{2} - \frac{1}{32 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{3} + \frac{3}{512 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 \cdot 2^{\frac{1}{2}} + \frac{\frac{3}{2 ^{\frac{1}{2}}}}{1 !} (x - 2) + \frac{\frac{3}{4 \cdot 2 ^{\frac{1}{2}}}}{2 !} (x - 2)^{2} + \frac{- \frac{3}{16 \cdot 2 ^{\frac{1}{2}}}}{3 !} (x - 2)^{3} + \frac{\frac{9}{64 \cdot 2 ^{\frac{1}{2}}}}{4 !} (x - 2)^{4} + \dots

Refine

= 2 \cdot 2^{\frac{1}{2}} + \frac{3}{2 ^{\frac{1}{2}}} (x - 2) + \frac{3}{8 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{2} - \frac{1}{32 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{3} + \frac{3}{512 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{4} + \dots

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