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Popular Calculus >

taylor x^{9/6},5

Solution

taylor

x^{\frac{9}{6}}, 5

Solution

5 \cdot 5^{\frac{1}{2}} + \frac{3 \cdot 5 ^{\frac{1}{2}}}{2} (x - 5) + \frac{3}{8 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{2} - \frac{1}{80 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{3} + \frac{3}{3200 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 5 \cdot 5^{\frac{1}{2}} + \frac{\frac{d}{d x} ( x ^{\frac{9}{6}} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{9}{6}} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{9}{6}} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

Evaluate Derivatives

= 5 \cdot 5^{\frac{1}{2}} + \frac{\frac{3 \cdot 5 ^{\frac{1}{2}}}{2}}{1 !} (x - 5) + \frac{\frac{3}{4 \cdot 5 ^{\frac{1}{2}}}}{2 !} (x - 5)^{2} + \frac{- \frac{3}{40 \cdot 5 ^{\frac{1}{2}}}}{3 !} (x - 5)^{3} + \frac{\frac{9}{400 \cdot 5 ^{\frac{1}{2}}}}{4 !} (x - 5)^{4} + \dots

Refine

= 5 \cdot 5^{\frac{1}{2}} + \frac{3 \cdot 5 ^{\frac{1}{2}}}{2} (x - 5) + \frac{3}{8 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{2} - \frac{1}{80 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{3} + \frac{3}{3200 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{4} + \dots

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