maclaurin 2^x

Lösung

maclaurin

2^{x}

1 + ln (2) x + \frac{ln ^{2} ( 2 )}{2} x^{2} + \frac{ln ^{3} ( 2 )}{6} x^{3} + \frac{ln ^{4} ( 2 )}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{ln ( 2 )}{1 !} x + \frac{ln ^{2} ( 2 )}{2 !} x^{2} + \frac{ln ^{3} ( 2 )}{3 !} x^{3} + \frac{ln ^{4} ( 2 )}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + ln (2) x + \frac{ln ^{2} ( 2 )}{2} x^{2} + \frac{ln ^{3} ( 2 )}{6} x^{3} + \frac{ln ^{4} ( 2 )}{24} x^{4} + \dots

\int y sin (x) d x

x \to π lim (sin (\frac{7}{6} x))

\int (x^{3} + 1)^{2} d x

d er i v a t i v e \frac{( x ^{2} - 2 x + 3 )}{( x - 1 ) ^{2}}

\frac{d}{d x} (e^{3 x} sin (2 x))