What is taylor 4cos(2x) ?

The answer to taylor 4cos(2x) is 4-8x^2+8/3 x^4-16/45 x^6+8/315 x^8+\ldots

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taylor 4cos(2x)

taylor

4 cos (2 x)

4 - 8 x^{2} + \frac{8}{3} x^{4} - \frac{16}{45} x^{6} + \frac{8}{315} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 4 + \frac{0}{1 !} x + \frac{- 16}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{64}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 256}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1024}{8 !} x^{8} + \dots

Refine

= 4 - 8 x^{2} + \frac{8}{3} x^{4} - \frac{16}{45} x^{6} + \frac{8}{315} x^{8} + \dots

f (x) = \frac{x}{( 3 x - 2 ) ^{4}}, at x = 1

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What is taylor 4cos(2x) ?
The answer to taylor 4cos(2x) is 4-8x^2+8/3 x^4-16/45 x^6+8/315 x^8+\ldots