What is taylor tan(x),0 ?

The answer to taylor tan(x),0 is x+1/3 x^3+2/15 x^5+17/315 x^7+62/2835 x^9+\ldots

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taylor tan(x),0

taylor

tan (x), 0

x + \frac{1}{3} x^{3} + \frac{2}{15} x^{5} + \frac{17}{315} x^{7} + \frac{62}{2835} x^{9} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( tan ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( tan ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( tan ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{2}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{16}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{272}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{7936}{9 !} x^{9} + \dots

Refine

= x + \frac{1}{3} x^{3} + \frac{2}{15} x^{5} + \frac{17}{315} x^{7} + \frac{62}{2835} x^{9} + \dots

y^{^{'}} - y = 1, y (0) = 0

x \to 0 lim (x ln (x - 1))

x^{2} - 2 x + 1, - x + 3

sec^{2} (x) d y + csc (y) d x = 0

(x e^{2 x})^{^{'}}

What is taylor tan(x),0 ?
The answer to taylor tan(x),0 is x+1/3 x^3+2/15 x^5+17/315 x^7+62/2835 x^9+\ldots