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Popular >

taylor \sqrt[4]{x},11

Solution

taylor

4 x, 11

Solution

411 + \frac{1}{4 \cdot 1 1 ^{\frac{3}{4}}} (x - 11) - \frac{3}{352 \cdot 1 1 ^{\frac{3}{4}}} (x - 11)^{2} + \frac{7}{15488 \cdot 1 1 ^{\frac{3}{4}}} (x - 11)^{3} - \frac{7}{247808 \cdot 1 1 ^{\frac{3}{4}}} (x - 11)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 411 + \frac{\frac{d}{d x} ( 4 x ) ( 11 )}{1 !} (x - 11) + \frac{\frac{d ^{2}}{d x ^{2}} ( 4 x ) ( 11 )}{2 !} (x - 11)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 4 x ) ( 11 )}{3 !} (x - 11)^{3} + \dots

Evaluate Derivatives

= 411 + \frac{\frac{1}{4 \cdot 1 1 ^{\frac{3}{4}}}}{1 !} (x - 11) + \frac{- \frac{3}{176 \cdot 1 1 ^{\frac{3}{4}}}}{2 !} (x - 11)^{2} + \frac{\frac{21}{7744 \cdot 1 1 ^{\frac{3}{4}}}}{3 !} (x - 11)^{3} + \frac{- \frac{21}{30976 \cdot 1 1 ^{\frac{3}{4}}}}{4 !} (x - 11)^{4} + \dots

Refine

= 411 + \frac{1}{4 \cdot 1 1 ^{\frac{3}{4}}} (x - 11) - \frac{3}{352 \cdot 1 1 ^{\frac{3}{4}}} (x - 11)^{2} + \frac{7}{15488 \cdot 1 1 ^{\frac{3}{4}}} (x - 11)^{3} - \frac{7}{247808 \cdot 1 1 ^{\frac{3}{4}}} (x - 11)^{4} + \dots

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