What is taylor sin(x^2),0 ?

The answer to taylor sin(x^2),0 is x^2-1/6 x^6+1/120 x^{10}+\ldots

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taylor sin(x^2),0

taylor

sin (x^{2}), 0

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

y^{^{''}} + y^{^{'}} - 2 y = sin (x)

\frac{d y}{d x} - y = e^{2 x} y^{3}

\frac{d ^{2} y}{d x ^{2}} + y = x^{2} + 2

\int \frac{1}{( t + 4 ) ( t - 1 )} d t

(x y - y^{2}) d x - x^{2} d y = 0

What is taylor sin(x^2),0 ?
The answer to taylor sin(x^2),0 is x^2-1/6 x^6+1/120 x^{10}+\ldots