What is taylor (x^2-1)cos(3x) ?

The answer to taylor (x^2-1)cos(3x) is -1+11/2 x^2-63/8 x^4+351/80 x^6-1053/896 x^8+\ldots

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taylor (x^2-1)cos(3x)

taylor

(x^{2} - 1) cos (3 x)

- 1 + \frac{11}{2} x^{2} - \frac{63}{8} x^{4} + \frac{351}{80} x^{6} - \frac{1053}{896} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - 1 + \frac{0}{1 !} x + \frac{11}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 189}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{3159}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 47385}{8 !} x^{8} + \dots

Refine

= - 1 + \frac{11}{2} x^{2} - \frac{63}{8} x^{4} + \frac{351}{80} x^{6} - \frac{1053}{896} x^{8} + \dots

x \to - 7 + lim (- \frac{8 x}{x + 7})

\frac{d}{d x} (\frac{3 x ^{2}}{2})

- 0.7 x^{2}

y = 6 x (9.18)

\frac{d}{d x} (\frac{2 x ^{5} + x ^{2} - 5}{x ^{2}})

What is taylor (x^2-1)cos(3x) ?
The answer to taylor (x^2-1)cos(3x) is -1+11/2 x^2-63/8 x^4+351/80 x^6-1053/896 x^8+\ldots