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Popular >

taylor sin(x), pi/5

Solution

taylor

sin (x), \frac{π}{5}

Solution

\frac{2 5 - 5}{4} + \frac{5 + 1}{4} (x - \frac{π}{5}) - \frac{5 - 5}{4 2} (x - \frac{π}{5})^{2} - \frac{5 + 1}{24} (x - \frac{π}{5})^{3} + \frac{5 - 5}{48 2} (x - \frac{π}{5})^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{2 5 - 5}{4} + \frac{\frac{d}{d x} ( sin ( x ) ) ( \frac{π}{5} )}{1 !} (x - \frac{π}{5}) + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( x ) ) ( \frac{π}{5} )}{2 !} (x - \frac{π}{5})^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( x ) ) ( \frac{π}{5} )}{3 !} (x - \frac{π}{5})^{3} + \dots

Evaluate Derivatives

= \frac{2 5 - 5}{4} + \frac{\frac{5 + 1}{4}}{1 !} (x - \frac{π}{5}) + \frac{- \frac{2 5 - 5}{4}}{2 !} (x - \frac{π}{5})^{2} + \frac{- \frac{5 + 1}{4}}{3 !} (x - \frac{π}{5})^{3} + \frac{\frac{2 5 - 5}{4}}{4 !} (x - \frac{π}{5})^{4} + \dots

Refine

= \frac{2 5 - 5}{4} + \frac{5 + 1}{4} (x - \frac{π}{5}) - \frac{5 - 5}{4 2} (x - \frac{π}{5})^{2} - \frac{5 + 1}{24} (x - \frac{π}{5})^{3} + \frac{5 - 5}{48 2} (x - \frac{π}{5})^{4} + \dots

Popular Examples

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

f (x) = 4^{2}

integral of ln(v)

\int ln (v) d v

(\partial)/(\partial x)(e^{-x^3})

\frac{\partial}{\partial x} (e^{- x^{3}})

tangent of f(x)= 3/(sqrt(x))tangent of

f (x) = \frac{3}{x}

(\partial)/(\partial y)(6x^{1/3}y^{2/3})

\frac{\partial}{\partial y} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

Frequently Asked Questions (FAQ)

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