maclaurin sec^2(x)

Lösung

maclaurin

sec^{2} (x)

1 + x^{2} + \frac{2}{3} x^{4} + \frac{17}{45} x^{6} + \frac{62}{315} x^{8} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 + x^{2} + \frac{2}{3} x^{4} + \frac{17}{45} x^{6} + \frac{62}{315} x^{8} + \dots

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