Re: [微積] 幾題~~

[JohnMash (Paul)]

※ 引述《dreamenjoy (今天也很爽)》之銘言：
: 2.Find a and b such that lim(sinax/x^3+b/x^2)=1/6
:                          x→0

   sin ax +bx = ax -(ax)^3/6 +...+bx

   hence a+b=0, -a^3=-1



:                                                        k
: 4.Find the interval of convergence of the series   (-1)      k
:                                                 Σ ———(x+2)
:                                                   　 2 k
:                                                  　 k 3

  if |x+2|>3 then a_k not convergent, hence S_k not convergent


  |a_{k+1}| / |a_k|

  =k^2/(k+1)^2/3*|x+2|

  for x=1, S=Σ(-1)/k^2, convergent

  for x=-5, S=Σ1/k^2, convergent

  for |x+2|/3 <1, absolutely convergent

  The answer is [-5,1]

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 112.104.96.9
→ dreamenjoy  :感恩!