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Popular >

taylor tan(x),3

Solution

taylor

tan (x), 3

Solution

tan (3) + sec^{2} (3) (x - 3) + sec^{2} (3) tan (3) (x - 3)^{2} + \frac{- 4 sec ^{2} ( 3 ) + 6 sec ^{4} ( 3 )}{6} (x - 3)^{3} + \frac{- 8 sec ^{2} ( 3 ) tan ( 3 ) + 24 sec ^{4} ( 3 ) tan ( 3 )}{24} (x - 3)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= tan (3) + \frac{sec ^{2} ( 3 )}{1 !} (x - 3) + \frac{2 sec ^{2} ( 3 ) tan ( 3 )}{2 !} (x - 3)^{2} + \frac{- 4 sec ^{2} ( 3 ) + 6 sec ^{4} ( 3 )}{3 !} (x - 3)^{3} + \frac{- 8 sec ^{2} ( 3 ) tan ( 3 ) + 24 sec ^{4} ( 3 ) tan ( 3 )}{4 !} (x - 3)^{4} + \dots

Refine

= tan (3) + sec^{2} (3) (x - 3) + sec^{2} (3) tan (3) (x - 3)^{2} + \frac{- 4 sec ^{2} ( 3 ) + 6 sec ^{4} ( 3 )}{6} (x - 3)^{3} + \frac{- 8 sec ^{2} ( 3 ) tan ( 3 ) + 24 sec ^{4} ( 3 ) tan ( 3 )}{24} (x - 3)^{4} + \dots

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Frequently Asked Questions (FAQ)

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