Question

求大神来解答高数题目

Answer 1

1. f(x) = ln(a+x) , a > 0
   f'(x) = 1/(a+x) = (1/a)/(1+x/a) = (1/a)∑<n=0,∞>(-1)^内n(x/a)^n
   = ∑<n=0,∞>[(-1)^n/a^(n+1)]x^n
   f(x) = ∫<0, x>f'(t)dt + f(0)
   = lna + ∑<n=0,∞>[(-1)^n/a^(n+1)]x^(n+1)/(n+1)
   收敛域 -1 < x/a < 1, -a < x < a。
   2. g(x) = (1/2)[e^x-e^(-x)]
   = (1/2)[∑<n=0,∞>x^n/n!容 - ∑<n=0,∞>(-x)^n/n!]
   = x/1! + x^3/3! + x^5/5! + ...... + x^(2k+1)/(2k+1)! + ......
   = ∑<n=0,∞>x^(2n+1)/(2n+1)!,
   收敛域： -∞ < x < +∞

   明白了吗？不明白找楼下给你解答

Answer 2

1. f(x) = ln(a+x) , a > 0
f'(x) = 1/(a+x) = (1/a)/(1+x/a) = (1/a)∑<n=0,∞>(-1)^n(x/a)^n
= ∑<n=0,∞>[(-1)^n/a^(n+1)]x^n
f(x) = ∫<0, x>f'(t)dt + f(0)
= lna + ∑<n=0,∞>[(-1)^n/a^(n+1)]x^(n+1)/(n+1)
收敛域 -1 < x/a < 1, -a < x < a。
2. g(x) = (1/2)[e^x-e^(-x)]
= (1/2)[∑<n=0,∞>x^n/n! - ∑<n=0,∞>(-x)^n/n!]
= x/1! + x^3/3! + x^5/5! + ...... + x^(2k+1)/(2k+1)! + ......
= ∑<n=0,∞>x^(2n+1)/(2n+1)!,
收敛域： -∞ < x < +∞