What is maclaurin sin(x^2), pi/4 ?

The answer to maclaurin sin(x^2), pi/4 is x^2-1/6 x^6+1/120 x^{10}+\ldots

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maclaurin sin(x^2), pi/4

maclaurin

sin (x^{2}), \frac{π}{4}

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

Solution steps

Apply the Maclaurin 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

n = 1 \sum \infty n \cdot (\frac{4}{5})^{n}

x \to 0 + lim (x (ln (x)))

4 x^{2} - 3 x + 2

\int_{1}^{3} x^{4} d x

f^{^{'}} (x) = 2 x + 3 x^{1.7}

What is maclaurin sin(x^2), pi/4 ?
The answer to maclaurin sin(x^2), pi/4 is x^2-1/6 x^6+1/120 x^{10}+\ldots