en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor 1/(sin(x))

Solution

taylor

\frac{1}{sin ( x )}

Solution

\frac{1}{sin ( 1 )} - cot (1) csc (1) (x - 1) + \frac{- csc ( 1 ) + 2 csc ^{3} ( 1 )}{2} (x - 1)^{2} + \frac{cot ( 1 ) csc ( 1 ) - 6 csc ^{3} ( 1 ) cot ( 1 )}{6} (x - 1)^{3} + \frac{csc ( 1 ) - 2 csc ^{3} ( 1 ) - 6 ( - 3 csc ^{3} ( 1 ) cot ^{2} ( 1 ) - csc ^{5} ( 1 ) )}{24} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{sin ( 1 )} + \frac{\frac{d}{d x} ( \frac{1}{s i n ( x )} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{s i n ( x )} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{s i n ( x )} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= \frac{1}{sin ( 1 )} + \frac{- cot ( 1 ) csc ( 1 )}{1 !} (x - 1) + \frac{- csc ( 1 ) + 2 csc ^{3} ( 1 )}{2 !} (x - 1)^{2} + \frac{cot ( 1 ) csc ( 1 ) - 6 csc ^{3} ( 1 ) cot ( 1 )}{3 !} (x - 1)^{3} + \frac{csc ( 1 ) - 2 csc ^{3} ( 1 ) - 6 ( - 3 csc ^{3} ( 1 ) cot ^{2} ( 1 ) - csc ^{5} ( 1 ) )}{4 !} (x - 1)^{4} + \dots

Refine

= \frac{1}{sin ( 1 )} - cot (1) csc (1) (x - 1) + \frac{- csc ( 1 ) + 2 csc ^{3} ( 1 )}{2} (x - 1)^{2} + \frac{cot ( 1 ) csc ( 1 ) - 6 csc ^{3} ( 1 ) cot ( 1 )}{6} (x - 1)^{3} + \frac{csc ( 1 ) - 2 csc ^{3} ( 1 ) - 6 ( - 3 csc ^{3} ( 1 ) cot ^{2} ( 1 ) - csc ^{5} ( 1 ) )}{24} (x - 1)^{4} + \dots

Popular Examples

taylor f(x)=e^{-2x}taylor

f (x) = e^{- 2 x}

derivative of e^{x+9}derivative of

e^{x + 9}

1/(x^2)(dy)/(dx)=25+14y

\frac{1}{x ^{2}} \frac{d y}{d x} = 25 + 14 y

derivative of f(x)=8sin(2x^4)derivative of

f (x) = 8 sin (2 x^{4})

tangent of f(x)=xsqrt(x),\at x=16 tangent of

f (x) = x x, at x = 16

Frequently Asked Questions (FAQ)

What is taylor 1/(sin(x)) ?
The answer to taylor 1/(sin(x)) is