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Beliebt Rechnen >

taylor 2^x

Lösung

taylor

2^{x}

Lösung

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 Taylor 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

Beliebte Beispiele

integral of (x^2+48x-16)/(x^3-16x)

derivative of 2^x+1

(dy)/(dt)=-y/(t^2)

tangent f(x)=6x-x^2,\at x=4

derivative of (x-5sin(x))