泰勒 cos(x)-x^2,1

解答

泰勒

cos (x) - x^{2}, 1

cos (1) - 1 + (- sin (1) - 2) (x - 1) + \frac{- cos ( 1 ) - 2}{2} (x - 1)^{2} + \frac{sin ( 1 )}{6} (x - 1)^{3} + \frac{cos ( 1 )}{24} (x - 1)^{4} + \dots

求解步骤

应用泰勒公式

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

求导数

= cos (1) - 1 + \frac{- sin ( 1 ) - 2}{1 !} (x - 1) + \frac{- cos ( 1 ) - 2}{2 !} (x - 1)^{2} + \frac{sin ( 1 )}{3 !} (x - 1)^{3} + \frac{cos ( 1 )}{4 !} (x - 1)^{4} + \dots

整理后得

= cos (1) - 1 + (- sin (1) - 2) (x - 1) + \frac{- cos ( 1 ) - 2}{2} (x - 1)^{2} + \frac{sin ( 1 )}{6} (x - 1)^{3} + \frac{cos ( 1 )}{24} (x - 1)^{4} + \dots

\int_{1}^{6} \frac{7 ln ( x )}{x ^{2}} d x

x \to 8 lim (2 x - 3)

\int_{1}^{3} 4 r^{4} ln (r) d r

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

\int ∣ x - 2 ∣ d x