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Popular >

taylor (sin(x))/x

Solution

taylor

\frac{sin ( x )}{x}

Solution

sin (1) + (cos (1) - sin (1)) (x - 1) + \frac{sin ( 1 ) - 2 cos ( 1 )}{2} (x - 1)^{2} + \frac{5 cos ( 1 ) - 3 sin ( 1 )}{6} (x - 1)^{3} + \frac{13 sin ( 1 ) - 20 cos ( 1 )}{24} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= sin (1) + \frac{cos ( 1 ) - sin ( 1 )}{1 !} (x - 1) + \frac{sin ( 1 ) - 2 cos ( 1 )}{2 !} (x - 1)^{2} + \frac{5 cos ( 1 ) - 3 sin ( 1 )}{3 !} (x - 1)^{3} + \frac{13 sin ( 1 ) - 20 cos ( 1 )}{4 !} (x - 1)^{4} + \dots

Refine

= sin (1) + (cos (1) - sin (1)) (x - 1) + \frac{sin ( 1 ) - 2 cos ( 1 )}{2} (x - 1)^{2} + \frac{5 cos ( 1 ) - 3 sin ( 1 )}{6} (x - 1)^{3} + \frac{13 sin ( 1 ) - 20 cos ( 1 )}{24} (x - 1)^{4} + \dots

Popular Examples

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(x^2-1)y^'=xyln(y)

(x^{2} - 1) y^{^{'}} = x y ln (y)

integral from 1 to infinity of x^{-4/3}

\int_{1}^{\infty} x^{- \frac{4}{3}} d x

Frequently Asked Questions (FAQ)

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