What is taylor cos(2x+(3pi)/2) ?

The answer to taylor cos(2x+(3pi)/2) is 2x-4/3 x^3+4/15 x^5-8/315 x^7+4/2835 x^9+\ldots

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taylor cos(2x+(3pi)/2)

taylor

cos (2 x + \frac{3 π}{2})

2 x - \frac{4}{3} x^{3} + \frac{4}{15} x^{5} - \frac{8}{315} x^{7} + \frac{4}{2835} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 8}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{32}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 128}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{512}{9 !} x^{9} + \dots

Refine

= 2 x - \frac{4}{3} x^{3} + \frac{4}{15} x^{5} - \frac{8}{315} x^{7} + \frac{4}{2835} x^{9} + \dots

\int \frac{1}{( 196 + x ^{2} ) ^{\frac{3}{2}}} d x

x \to - 1 lim (g (x))

15 e^{3 x}

x \to 3 lim (x)

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 12, y^{^{'}} (0) = - 3

What is taylor cos(2x+(3pi)/2) ?
The answer to taylor cos(2x+(3pi)/2) is 2x-4/3 x^3+4/15 x^5-8/315 x^7+4/2835 x^9+\ldots