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Popular >

taylor 1/(1-x),(pi/4)

Solution

taylor

\frac{1}{1 - x}, (\frac{π}{4})

Solution

\frac{4}{4 - π} + \frac{16}{( 4 - π ) ^{2}} (x - (\frac{π}{4})) + \frac{64}{( 4 - π ) ^{3}} (x - (\frac{π}{4}))^{2} + \frac{256}{( 4 - π ) ^{4}} (x - (\frac{π}{4}))^{3} + \frac{1024}{( 4 - π ) ^{5}} (x - (\frac{π}{4}))^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{4}{4 - π} + \frac{\frac{16}{( 4 - π ) ^{2}}}{1 !} (x - (\frac{π}{4})) + \frac{\frac{128}{( 4 - π ) ^{3}}}{2 !} (x - (\frac{π}{4}))^{2} + \frac{\frac{1536}{( 4 - π ) ^{4}}}{3 !} (x - (\frac{π}{4}))^{3} + \frac{\frac{24576}{( 4 - π ) ^{5}}}{4 !} (x - (\frac{π}{4}))^{4} + \dots

Refine

= \frac{4}{4 - π} + \frac{16}{( 4 - π ) ^{2}} (x - (\frac{π}{4})) + \frac{64}{( 4 - π ) ^{3}} (x - (\frac{π}{4}))^{2} + \frac{256}{( 4 - π ) ^{4}} (x - (\frac{π}{4}))^{3} + \frac{1024}{( 4 - π ) ^{5}} (x - (\frac{π}{4}))^{4} + \dots

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Frequently Asked Questions (FAQ)

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