What is taylor x^3cos(x^4) ?

The answer to taylor x^3cos(x^4) is x^3+\ldots

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taylor x^3cos(x^4)

taylor

x^{3} cos (x^{4})

x^{3} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= x^{3} + \dots

x \to \infty lim (m x + b)

e^{- 5 s} \cdot \frac{1}{s ^{2}}

y^{^{'}} - 3 y = - 3 x

\frac{\partial}{\partial x} (5 y cos (- 9 x))

\int_{- \infty}^{- 1} e^{- 26 t} d t