What is maclaurin (x^2+3)cos(-3x) ?

The answer to maclaurin (x^2+3)cos(-3x) is 3-25/2 x^2+45/8 x^4+27/80 x^6-2349/4480 x^8+\ldots

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maclaurin (x^2+3)cos(-3x)

maclaurin

(x^{2} + 3) cos (- 3 x)

3 - \frac{25}{2} x^{2} + \frac{45}{8} x^{4} + \frac{27}{80} x^{6} - \frac{2349}{4480} x^{8} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 3 + \frac{0}{1 !} x + \frac{- 25}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{135}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{243}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 21141}{8 !} x^{8} + \dots

Refine

= 3 - \frac{25}{2} x^{2} + \frac{45}{8} x^{4} + \frac{27}{80} x^{6} - \frac{2349}{4480} x^{8} + \dots

x \to 2 π + lim (x csc (x))

\int_{2}^{3} \frac{15}{3 - x} d x

- x^{2} + y = 1, [2, - 2]

\int (r^{2} + r + 1) e^{r} d r

What is maclaurin (x^2+3)cos(-3x) ?
The answer to maclaurin (x^2+3)cos(-3x) is 3-25/2 x^2+45/8 x^4+27/80 x^6-2349/4480 x^8+\ldots