What is maclaurin sin(x^4) ?

The answer to maclaurin sin(x^4) is x^4+\ldots

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maclaurin sin(x^4)

maclaurin

sin (x^{4})

x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( sin ( x ^{4} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( x ^{4} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( x ^{4} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= x^{4} + \dots

\int_{0}^{7} \frac{3 t}{( t - 8 ) ^{2}} d t

f (x) = \frac{2}{3 x + 5}, at a = - 1

\int_{0}^{4} π (4 x - x^{2}) d x

x sin (- 2 x) π