What is taylor arctan(4x) ?

The answer to taylor arctan(4x) is 4x-64/3 x^3+1024/5 x^5-16384/7 x^7+262144/9 x^9+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor arctan(4x)

taylor

arctan (4 x)

4 x - \frac{64}{3} x^{3} + \frac{1024}{5} x^{5} - \frac{16384}{7} x^{7} + \frac{262144}{9} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{4}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 128}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{24576}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 11796480}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{10569646080}{9 !} x^{9} + \dots

Refine

= 4 x - \frac{64}{3} x^{3} + \frac{1024}{5} x^{5} - \frac{16384}{7} x^{7} + \frac{262144}{9} x^{9} + \dots

\int \frac{2}{8 - 5 x} d x

f (x) = x^{\frac{1}{2}} (x^{2} - x + 3), at x = 1

(27 + x^{2}) y^{^{'}} - 2 x y = 0

\int (\frac{x}{10})^{n} d x

\int 8 e^{2 x} sin (2 x) d x

What is taylor arctan(4x) ?
The answer to taylor arctan(4x) is 4x-64/3 x^3+1024/5 x^5-16384/7 x^7+262144/9 x^9+\ldots