What is taylor sin(x^2) ?

The answer to taylor sin(x^2) is x^2-1/6 x^6+1/120 x^{10}+\ldots

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taylor sin(x^2)

taylor

sin (x^{2})

x^{2} - \frac{1}{6} x^{6} + \frac{1}{120} x^{10} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 120}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{30240}{10 !} x^{10} + \dots

Refine

= x^{2} - \frac{1}{6} x^{6} + \frac{1}{120} x^{10} + \dots

\frac{d}{d x} (\frac{3 x - 4}{x + 2})

\int \frac{1}{3 x - 1} d x

\int_{- 4}^{4} 4 - x^{2} d x

\int (x^{\frac{4}{3}} + 4 x^{\frac{1}{3}}) d x

x \to 3 lim (cos (π (x)) + 6)

What is taylor sin(x^2) ?
The answer to taylor sin(x^2) is x^2-1/6 x^6+1/120 x^{10}+\ldots