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Popular >

taylor (7-3x^2)^{1/2},0

Solution

taylor

(7 - 3 x^{2})^{\frac{1}{2}}, 0

Solution

7^{\frac{1}{2}} - \frac{3}{2 \cdot 7 ^{\frac{1}{2}}} x^{2} - \frac{9}{56 \cdot 7 ^{\frac{1}{2}}} x^{4} - \frac{27}{784 \cdot 7 ^{\frac{1}{2}}} x^{6} - \frac{405}{43904 \cdot 7 ^{\frac{1}{2}}} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 7^{\frac{1}{2}} + \frac{\frac{d}{d x} ( ( 7 - 3 x ^{2} ) ^{\frac{1}{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 7 - 3 x ^{2} ) ^{\frac{1}{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 7 - 3 x ^{2} ) ^{\frac{1}{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 7^{\frac{1}{2}} + \frac{0}{1 !} x + \frac{- \frac{3}{7 ^{\frac{1}{2}}}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- \frac{27}{7 \cdot 7 ^{\frac{1}{2}}}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- \frac{1215}{49 \cdot 7 ^{\frac{1}{2}}}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- \frac{18225}{49 \cdot 7 ^{\frac{1}{2}}}}{8 !} x^{8} + \dots

Refine

= 7^{\frac{1}{2}} - \frac{3}{2 \cdot 7 ^{\frac{1}{2}}} x^{2} - \frac{9}{56 \cdot 7 ^{\frac{1}{2}}} x^{4} - \frac{27}{784 \cdot 7 ^{\frac{1}{2}}} x^{6} - \frac{405}{43904 \cdot 7 ^{\frac{1}{2}}} x^{8} + \dots

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Frequently Asked Questions (FAQ)

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