What is taylor cos(3x)2.5 ?

The answer to taylor cos(3x)2.5 is 2.5-11.25x^2+8.4375x^4-2.53125x^6+0.40680…x^8+\ldots

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taylor cos(3x)2.5

taylor

cos (3 x) 2.5

2.5 - 11.25 x^{2} + 8.4375 x^{4} - 2.53125 x^{6} + 0.40680 \dots x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 2.5 + \frac{\frac{d}{d x} ( cos ( 3 x ) \cdot 2.5 ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( 3 x ) \cdot 2.5 ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( 3 x ) \cdot 2.5 ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 2.5 + \frac{0}{1 !} x + \frac{- 22.5}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{202.5}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 1822.5}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{16402.5}{8 !} x^{8} + \dots

Refine

= 2.5 - 11.25 x^{2} + 8.4375 x^{4} - 2.53125 x^{6} + 0.40680 \dots x^{8} + \dots

\frac{\partial}{\partial x} (6 x + y^{2})

n = 1 \sum \infty \frac{6 n !}{n ^{n}}

\frac{d}{d x} (\frac{x ^{2} - 5}{1 - 3 x ^{2}})

6 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\frac{d}{d x} (\frac{x ^{2} tan ( x ^{3} - x ^{2} )}{sec ( x )})

What is taylor cos(3x)2.5 ?
The answer to taylor cos(3x)2.5 is 2.5-11.25x^2+8.4375x^4-2.53125x^6+0.40680…x^8+\ldots