What is taylor sin(4x) ?

The answer to taylor sin(4x) is 4x-32/3 x^3+128/15 x^5-1024/315 x^7+2048/2835 x^9+\ldots

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taylor sin(4x)

taylor

sin (4 x)

4 x - \frac{32}{3} x^{3} + \frac{128}{15} x^{5} - \frac{1024}{315} x^{7} + \frac{2048}{2835} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{4}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 64}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{1024}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 16384}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{262144}{9 !} x^{9} + \dots

Refine

= 4 x - \frac{32}{3} x^{3} + \frac{128}{15} x^{5} - \frac{1024}{315} x^{7} + \frac{2048}{2835} x^{9} + \dots

\int - \frac{e ^{4 x}}{4 x} d x

\int \frac{cos ( 4 x )}{2 + sin ( 4 x )} d x

f (x) = x sin (2 x^{2})

\frac{e ^{x}}{5 + e ^{x}}

\int_{- 2}^{3} ∣ x ∣ d x

What is taylor sin(4x) ?
The answer to taylor sin(4x) is 4x-32/3 x^3+128/15 x^5-1024/315 x^7+2048/2835 x^9+\ldots