What is taylor x^5cos(x^3) ?

The answer to taylor x^5cos(x^3) is x^5+\ldots

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taylor x^5cos(x^3)

taylor

x^{5} cos (x^{3})

x^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( x ^{5} cos ( x ^{3} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{5} cos ( x ^{3} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{5} cos ( x ^{3} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{120}{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^{5} + \dots

\frac{d}{d x} ((2 x^{2} + 7)^{5})

x \to 0 lim ((e^{x} + x)^{\frac{5}{x}})

\int sin^{2} (2 π x) d x

x \to - 2 lim (\frac{x - 2}{∣ x - 2 ∣})

x \to 0 lim (\frac{cos ( π x )}{x})