maclaurin e^{2x}

Lösung

maclaurin

e^{2 x}

1 + 2 x + 2 x^{2} + \frac{4}{3} x^{3} + \frac{2}{3} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{4}{2 !} x^{2} + \frac{8}{3 !} x^{3} + \frac{16}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + 2 x + 2 x^{2} + \frac{4}{3} x^{3} + \frac{2}{3} x^{4} + \dots

in v erse l a pl a ce \frac{- 2}{s + 3}

d er i v a t i v e f (x) = sin (sin (sin (x)))

\frac{d}{d x} (ln (\frac{x ^{2} - 7}{x}))

x \to 0 lim (\frac{( x + h ) ^{3} - x}{h})

\frac{d y}{d x} + y = e^{3 x}