maclaurin tan(θ)

Lösung

maclaurin

tan (θ)

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

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

x \to 9 + lim (\frac{∣ x - 9 ∣}{x - 9})

x \to 0 lim (cot (\frac{π}{2} - x))

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