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Popular >

taylor sin(x^{0.5})

Solution

taylor

sin (x^{0.5})

Solution

sin (1) + \frac{cos ( 1 )}{2} (x - 1) + \frac{- sin ( 1 ) - cos ( 1 )}{8} (x - 1)^{2} - \frac{- 2 cos ( 1 ) - 3 sin ( 1 )}{48} (x - 1)^{3} - \frac{9 cos ( 1 ) + 14 sin ( 1 )}{384} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= sin (1) + \frac{\frac{c o s ( 1 )}{2}}{1 !} (x - 1) + \frac{\frac{- s i n ( 1 ) - c o s ( 1 )}{4}}{2 !} (x - 1)^{2} + \frac{- \frac{- 2 c o s ( 1 ) - 3 s i n ( 1 )}{8}}{3 !} (x - 1)^{3} + \frac{- \frac{9 c o s ( 1 ) + 14 s i n ( 1 )}{16}}{4 !} (x - 1)^{4} + \dots

Refine

= sin (1) + \frac{cos ( 1 )}{2} (x - 1) + \frac{- sin ( 1 ) - cos ( 1 )}{8} (x - 1)^{2} - \frac{- 2 cos ( 1 ) - 3 sin ( 1 )}{48} (x - 1)^{3} - \frac{9 cos ( 1 ) + 14 sin ( 1 )}{384} (x - 1)^{4} + \dots

Popular Examples

derivative of (x^2+1)(2x+5+8/x)derivative of

(x^{2} + 1) (2 x + 5 + \frac{8}{x})

derivative of y=(x^2-4x)/(x+1)derivative of

y = \frac{x ^{2} - 4 x}{x + 1}

integral of 8xcos(3x)

\int 8 x cos (3 x) d x

derivative of cos(kx)

\frac{d}{d x} (cos (k x))

integral of (sqrt(1+sin(x)))/(sec(x))

\int \frac{1 + sin ( x )}{sec ( x )} d x

Frequently Asked Questions (FAQ)

What is taylor sin(x^{0.5}) ?
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