maclaurin arccos((cos(x))/(1+cos(x)))

Lösung

maclaurin

arccos (\frac{cos ( x )}{1 + cos ( x )})

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

Schritte zur Lösung

Apply the Maclaurin Formula

= \frac{π}{3} + \frac{\frac{d}{d x} ( arccos ( \frac{c o s ( x )}{1 + c o s ( x )} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( arccos ( \frac{c o s ( x )}{1 + c o s ( x )} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( arccos ( \frac{c o s ( x )}{1 + c o s ( x )} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{π}{3} + \frac{0}{1 !} x + \frac{\frac{1}{2 3}}{2 !} x^{2} + \dots

Fasse zusammen

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

f (x) = sin (8 x)

d er i v a t i v e y = x^{9 c o s (x)}

\int 2 - ∣ x ∣ d x

\frac{d}{d x} ((x^{3} + x^{2} - 2) (7 + x - x^{4}))

\int \frac{( 3 ( 4 u + 1 ) ^{\frac{1}{2}} )}{4} d u