What is taylor 2sqrt(9+x^2) ?

The answer to taylor 2sqrt(9+x^2) is 6+1/3 x^2-1/108 x^4+1/1944 x^6-5/139968 x^8+\ldots

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taylor 2sqrt(9+x^2)

taylor

2 9 + x^{2}

6 + \frac{1}{3} x^{2} - \frac{1}{108} x^{4} + \frac{1}{1944} x^{6} - \frac{5}{139968} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 6 + \frac{\frac{d}{d x} ( 2 9 + x ^{2} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 2 9 + x ^{2} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 2 9 + x ^{2} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 6 + \frac{0}{1 !} x + \frac{\frac{2}{3}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- \frac{2}{9}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{\frac{10}{27}}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- \frac{350}{243}}{8 !} x^{8} + \dots

Refine

= 6 + \frac{1}{3} x^{2} - \frac{1}{108} x^{4} + \frac{1}{1944} x^{6} - \frac{5}{139968} x^{8} + \dots

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What is taylor 2sqrt(9+x^2) ?
The answer to taylor 2sqrt(9+x^2) is 6+1/3 x^2-1/108 x^4+1/1944 x^6-5/139968 x^8+\ldots