taylor e^{cos(sin(x^2))}

Lösung

taylor

e^{c o s (s i n (x^{2}))}

e + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= e + \dots

\int_{- 1}^{1} - 1 d x

\int (x - \frac{1}{x})^{2} d x

\frac{\partial}{\partial x} (e^{- 1})

x \to 3 lim (x^{2} - 6 x + 8)

\int \frac{1}{t ^{2} 4 - t ^{2}} d t