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1、常用的泰勒公式 常用的泰勒公式 ex = 1+x+x2/2!+x3/3!+xn/n!+ ln(1+x)=x-x2/2+x3/3-+(-1)(k-1)*(xk)/k(|x|1) sin x = x-x3/3!+x5/5!-+(-1)(k-1)*(x(2k-1)/(2k-1)!+。(-x) cos x = 1-x2/2!+x4/4!-+(-1)k*(x(2k)/(2k)!+ (-x) tanx=x+x3/3+2x5/15+17x7/315+62x9/2835+2(2n)*(2(2n)-1)*B(2n-1)*x(2n-1)/(2n)!+.(|x|/2) arcsin x = x + 1/2*x3/3
2、 + 1*3/(2*4)*x5/5 + (|x|1) arccos x = - ( x + 1/2*x3/3 + 1*3/(2*4)*x5/5 + ) (|x|1) arctan x = x - x3/3 + x5/5 -(x1) sh x = x+x3/3!+x5/5!+(-1)(k-1)*(x2k-1)/(2k-1)!+ (-x) ch x = 1+x2/2!+x4/4!+(-1)k*(x2k)/(2k)!+(-x) arcsh x = x - 1/2*x3/3 + 1*3/(2*4)*x5/5 - (|x|1) arcth x = x + x3/3 + x5/5 + (|x|1) mm(m-1)2m(m-1)(m-2)3(1+z)m=1m1+z+z+z+1!2!3!,(z1)
