taylor 5x^3-6x^2+12x-3,3

Lösung

taylor

5 x^{3} - 6 x^{2} + 12 x - 3, 3

114 + 111 (x - 3) + 39 (x - 3)^{2} + 5 (x - 3)^{3}

Schritte zur Lösung

Apply the Taylor Formula

= 114 + \frac{\frac{d}{d x} ( 5 x ^{3} - 6 x ^{2} + 12 x - 3 ) ( 3 )}{1 !} (x - 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( 5 x ^{3} - 6 x ^{2} + 12 x - 3 ) ( 3 )}{2 !} (x - 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 5 x ^{3} - 6 x ^{2} + 12 x - 3 ) ( 3 )}{3 !} (x - 3)^{3} + \dots

Evaluate Derivatives

= 114 + \frac{111}{1 !} (x - 3) + \frac{78}{2 !} (x - 3)^{2} + \frac{30}{3 !} (x - 3)^{3} + \frac{0}{4 !} (x - 3)^{4} + \frac{0}{5 !} (x - 3)^{5} + \frac{0}{6 !} (x - 3)^{6} + \frac{0}{7 !} (x - 3)^{7} + \frac{0}{8 !} (x - 3)^{8} + \frac{0}{9 !} (x - 3)^{9} + \frac{0}{10 !} (x - 3)^{10}

Fasse zusammen

= 114 + 111 (x - 3) + 39 (x - 3)^{2} + 5 (x - 3)^{3}

\frac{d}{d x} (4 x^{3} + 3 x^{2} - 6 x + 1)

x \to 0 + lim (\frac{4}{x ^{2} - x})

\frac{\partial}{\partial y} (y e^{x y} + y)

d er i v a t i v e x^{3} - 5 x^{2} + 13

\frac{d}{d x} (e^{s i n (x)})