What is taylor tan(x),-pi/4 ?

The answer to taylor tan(x),-pi/4 is -1+2(x+pi/4)-2(x+pi/4)^2+8/3 (x+pi/4)^3-10/3 (x+pi/4)^4+\ldots

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taylor tan(x),-pi/4

taylor

tan (x), - \frac{π}{4}

- 1 + 2 (x + \frac{π}{4}) - 2 (x + \frac{π}{4})^{2} + \frac{8}{3} (x + \frac{π}{4})^{3} - \frac{10}{3} (x + \frac{π}{4})^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - 1 + \frac{2}{1 !} (x + \frac{π}{4}) + \frac{- 4}{2 !} (x + \frac{π}{4})^{2} + \frac{16}{3 !} (x + \frac{π}{4})^{3} + \frac{- 80}{4 !} (x + \frac{π}{4})^{4} + \dots

Refine

= - 1 + 2 (x + \frac{π}{4}) - 2 (x + \frac{π}{4})^{2} + \frac{8}{3} (x + \frac{π}{4})^{3} - \frac{10}{3} (x + \frac{π}{4})^{4} + \dots

What is taylor tan(x),-pi/4 ?
The answer to taylor tan(x),-pi/4 is -1+2(x+pi/4)-2(x+pi/4)^2+8/3 (x+pi/4)^3-10/3 (x+pi/4)^4+\ldots