What is taylor arctan(x/2) ?

The answer to taylor arctan(x/2) is 1/2 x-1/24 x^3+1/160 x^5-1/896 x^7+1/4608 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(x/2)

taylor

arctan (\frac{x}{2})

\frac{1}{2} x - \frac{1}{24} x^{3} + \frac{1}{160} x^{5} - \frac{1}{896} x^{7} + \frac{1}{4608} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{\frac{1}{2}}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- \frac{1}{4}}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{\frac{3}{4}}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- \frac{45}{8}}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{\frac{315}{4}}{9 !} x^{9} + \dots

Refine

= \frac{1}{2} x - \frac{1}{24} x^{3} + \frac{1}{160} x^{5} - \frac{1}{896} x^{7} + \frac{1}{4608} x^{9} + \dots

2 y^{^{''}} + 50 y = 0

\int 1 - \frac{2 x}{x ^{2} + 1} d x

\int \frac{x ^{3} - 2 x ^{4} + x ^{5}}{2} d x

3 tan (x)

f (x) = 12 x, (9, 36)

What is taylor arctan(x/2) ?
The answer to taylor arctan(x/2) is 1/2 x-1/24 x^3+1/160 x^5-1/896 x^7+1/4608 x^9+\ldots