What is maclaurin arctan(x^2) ?

The answer to maclaurin arctan(x^2) is x^2-1/3 x^6+1/5 x^{10}+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

maclaurin arctan(x^2)

maclaurin

arctan (x^{2})

x^{2} - \frac{1}{3} x^{6} + \frac{1}{5} x^{10} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 240}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{725760}{10 !} x^{10} + \dots

Refine

= x^{2} - \frac{1}{3} x^{6} + \frac{1}{5} x^{10} + \dots

\int_{1}^{2} e^{- x} d x

4 x = y^{2} + 12, 3 \leq x \leq 11

\int_{0}^{\frac{π}{2}} ∣ 7 sin (x) - 7 cos (2 x) ∣ d x

y = \frac{2}{x ^{2}}

What is maclaurin arctan(x^2) ?
The answer to maclaurin arctan(x^2) is x^2-1/3 x^6+1/5 x^{10}+\ldots