maclaurin (1-e^{-ax})^2

Lösung

maclaurin

(1 - e^{- a x})^{2}

a^{2} x^{2} - a^{3} x^{3} + \frac{7 a ^{4}}{12} x^{4} - \frac{a ^{5}}{4} x^{5} + \frac{31 a ^{6}}{360} x^{6} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2 a ^{2}}{2 !} x^{2} + \frac{- 6 a ^{3}}{3 !} x^{3} + \frac{14 a ^{4}}{4 !} x^{4} + \frac{- 30 a ^{5}}{5 !} x^{5} + \frac{62 a ^{6}}{6 !} x^{6} + \dots

Fasse zusammen

= a^{2} x^{2} - a^{3} x^{3} + \frac{7 a ^{4}}{12} x^{4} - \frac{a ^{5}}{4} x^{5} + \frac{31 a ^{6}}{360} x^{6} + \dots

in v erse l a pl a ce \frac{3 e ^{(- 2 s)}}{( s ^{2} - 4 s + 3 )}

d er i v a t i v e ln (100 sin^{2} (x))

d er i v a t i v e f (x) = \frac{4 x ^{2} tan ( x )}{sec ( x )}

x \to - 2 lim (- 0.8)

x d y - y d x = (2 x^{2} - 3) d x