What is taylor cos(x^4) ?

The answer to taylor cos(x^4) is 1-1/2 x^8+\ldots

Popular >

taylor cos(x^4)

taylor

cos (x^{4})

1 - \frac{1}{2} x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 20160}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 - \frac{1}{2} x^{8} + \dots

(- sin (3 x) \cdot 3)^{^{'}}

x \to \infty lim (\frac{( e ^{2 x} )}{x ^{2}})

\frac{d y}{d x} = \frac{x}{y} + \frac{y}{x}

\frac{\partial}{\partial x} ((x^{2} + 2 y^{2} + 3 z^{2}) e^{- (x^{2} + y^{2} + z^{2})})

\int e^{\frac{x ^{2}}{2}} x^{3} d x