What is taylor x+(x^3)/3-tan(x) ?

The answer to taylor x+(x^3)/3-tan(x) is -2/15 x^5-17/315 x^7-62/2835 x^9+\ldots

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taylor x+(x^3)/3-tan(x)

taylor

x + \frac{x ^{3}}{3} - tan (x)

- \frac{2}{15} x^{5} - \frac{17}{315} x^{7} - \frac{62}{2835} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 16}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 272}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 7936}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= - \frac{2}{15} x^{5} - \frac{17}{315} x^{7} - \frac{62}{2835} x^{9} + \dots

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What is taylor x+(x^3)/3-tan(x) ?
The answer to taylor x+(x^3)/3-tan(x) is -2/15 x^5-17/315 x^7-62/2835 x^9+\ldots