What is maclaurin x^2sin(x) ?

The answer to maclaurin x^2sin(x) is x^3-1/6 x^5+1/120 x^7-1/5040 x^9+\ldots

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maclaurin x^2sin(x)

maclaurin

x^{2} sin (x)

x^{3} - \frac{1}{6} x^{5} + \frac{1}{120} x^{7} - \frac{1}{5040} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 20}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{42}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 72}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= x^{3} - \frac{1}{6} x^{5} + \frac{1}{120} x^{7} - \frac{1}{5040} x^{9} + \dots

\frac{d}{d x} ((x - cos (x)) sin (x))

4 x^{3} - 5 x + 3

x \to 0 lim ((\frac{1}{x}) sin (x))

y = \frac{25}{2} - \frac{x ^{2}}{2}, (- 5, 5)

\frac{d}{d x} (5 - 3 x)

What is maclaurin x^2sin(x) ?
The answer to maclaurin x^2sin(x) is x^3-1/6 x^5+1/120 x^7-1/5040 x^9+\ldots