en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor sec(x)

Solution

taylor

sec (x)

Solution

sec (1) + sec (1) tan (1) (x - 1) + \frac{- sec ( 1 ) + 2 sec ^{3} ( 1 )}{2} (x - 1)^{2} + \frac{- sec ( 1 ) + 6 sec ^{3} ( 1 )}{6 cot ( 1 )} (x - 1)^{3} + \frac{cot ( 1 ) ( - sec ( 1 ) tan ( 1 ) + 18 sec ^{3} ( 1 ) tan ( 1 ) ) + csc ^{2} ( 1 ) ( - sec ( 1 ) + 6 sec ^{3} ( 1 ) )}{24 cot ^{2} ( 1 )} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= sec (1) + \frac{sec ( 1 ) tan ( 1 )}{1 !} (x - 1) + \frac{- sec ( 1 ) + 2 sec ^{3} ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{- s e c ( 1 ) + 6 s e c ^{3} ( 1 )}{c o t ( 1 )}}{3 !} (x - 1)^{3} + \frac{\frac{c o t ( 1 ) ( - s e c ( 1 ) t a n ( 1 ) + 18 s e c ^{3} ( 1 ) t a n ( 1 ) ) + c s c ^{2} ( 1 ) ( - s e c ( 1 ) + 6 s e c ^{3} ( 1 ) )}{c o t ^{2} ( 1 )}}{4 !} (x - 1)^{4} + \dots

Refine

= sec (1) + sec (1) tan (1) (x - 1) + \frac{- sec ( 1 ) + 2 sec ^{3} ( 1 )}{2} (x - 1)^{2} + \frac{- sec ( 1 ) + 6 sec ^{3} ( 1 )}{6 cot ( 1 )} (x - 1)^{3} + \frac{cot ( 1 ) ( - sec ( 1 ) tan ( 1 ) + 18 sec ^{3} ( 1 ) tan ( 1 ) ) + csc ^{2} ( 1 ) ( - sec ( 1 ) + 6 sec ^{3} ( 1 ) )}{24 cot ^{2} ( 1 )} (x - 1)^{4} + \dots

Popular Examples

integral of x/(x^3+1)

\int \frac{x}{x ^{3} + 1} d x

integral of sin(x)+sin(x)cos(x)

\int sin (x) + sin (x) cos (x) d x

integral of (4sqrt(x))/(x^3+1)

\int \frac{4 x}{x ^{3} + 1} d x

integral of (4x^2+1)^3*8x

\int (4 x^{2} + 1)^{3} \cdot 8 x d x

derivative of sqrt(x)(1-x^2)derivative of

x (1 - x^{2})

Frequently Asked Questions (FAQ)

What is taylor sec(x) ?
The answer to taylor sec(x) is