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Popular >

taylor sin(x), pi/3

Solution

taylor

sin (x), \frac{π}{3}

Solution

\frac{3}{2} + \frac{1}{2} (x - \frac{π}{3}) - \frac{3}{4} (x - \frac{π}{3})^{2} - \frac{1}{12} (x - \frac{π}{3})^{3} + \frac{1}{16 3} (x - \frac{π}{3})^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{3}{2} + \frac{\frac{1}{2}}{1 !} (x - \frac{π}{3}) + \frac{- \frac{3}{2}}{2 !} (x - \frac{π}{3})^{2} + \frac{- \frac{1}{2}}{3 !} (x - \frac{π}{3})^{3} + \frac{\frac{3}{2}}{4 !} (x - \frac{π}{3})^{4} + \dots

Refine

= \frac{3}{2} + \frac{1}{2} (x - \frac{π}{3}) - \frac{3}{4} (x - \frac{π}{3})^{2} - \frac{1}{12} (x - \frac{π}{3})^{3} + \frac{1}{16 3} (x - \frac{π}{3})^{4} + \dots

Popular Examples

limit as x approaches 64 of x^{3/2}

x \to 64 lim (x^{\frac{3}{2}})

limit as x approaches 0 of (2x^2-3x)/x

x \to 0 lim (\frac{2 x ^{2} - 3 x}{x})

inverse oflaplace e^{-3t}inverse laplace

e^{- 3 t}

derivative of (ax^2+bx+ce^{-x/8})

\frac{d}{d x} ((a x^{2} + b x + c) e^{- \frac{x}{8}})

limit as x approaches-1 of-x^2+4x

x \to - 1 lim (- x^{2} + 4 x)

Frequently Asked Questions (FAQ)

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