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Popular Calculus >

taylor sin(x),(pi/4)

Solution

taylor

sin (x), (\frac{π}{4})

Solution

\frac{2}{2} + \frac{1}{2} (x - (\frac{π}{4})) - \frac{1}{2 2} (x - (\frac{π}{4}))^{2} - \frac{1}{6 2} (x - (\frac{π}{4}))^{3} + \frac{1}{24 2} (x - (\frac{π}{4}))^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= \frac{2}{2} + \frac{1}{2} (x - (\frac{π}{4})) - \frac{1}{2 2} (x - (\frac{π}{4}))^{2} - \frac{1}{6 2} (x - (\frac{π}{4}))^{3} + \frac{1}{24 2} (x - (\frac{π}{4}))^{4} + \dots

Popular Examples

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y^{^{'''}} - 6 y^{^{''}} = 4 - cos (x)

limit as x approaches 2+of x/(x^2-4)

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

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\int \frac{x ^{3} + 1}{x + 1} d x

limit as x approaches 3-of 3/(x-3)

x \to 3 - lim (\frac{3}{x - 3})

Frequently Asked Questions (FAQ)

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