taylor e^{x^5},0

Lösung

taylor

e^{x^{5}}, 0

1 + x^{5} + \frac{1}{2} x^{10} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( e ^{x^{5}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{x^{5}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{x^{5}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{120}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{1814400}{10 !} x^{10} + \dots

Fasse zusammen

= 1 + x^{5} + \frac{1}{2} x^{10} + \dots

x \to 1 lim (x^{2} - 4)

x \to 0 lim ((1 - 2 x)^{\frac{1}{x}})

\int \frac{1}{3 - 2 x ^{2}} d x

d er i v a t i v e sin (x) ln (5 x)

d er i v a t i v e 2 e^{x^{3}} + 1