Re: [積分] 求體積還有幾個問題

[LuisSantos ( )]

※ 引述《ggyy340 (阿甘)》之銘言：
:   Find the volume bounded by the sphere x^2+y^2+z^2=9
: and the paraboloid x^2+y^2=8z
: 不會算....
: Show that lim  (1+c/n^2)^n=1
:           n→∞

              c
  lim  (1 + -----)^n
  n→∞      n^2

                        1             1
= lim (1 + (c)*(y^2))^(---)  (令 y = --- , 當n→∞時 , y→0)
  y→0                  y             n

                               1
= lim  e^(ln((1 + (c)*(y^2))^(---)))
  y→0                         y

                               1
= e^(lim  ln((1 + (c)*(y^2))^(---)))
     y→0                      y

           ln(1 + (c)*(y^2))
= e^(lim  -------------------)
     y→0        y

           ((2c)*(y))/(1 + (c)*(y^2))
= e^(lim  ----------------------------)
     y→0      1

             2c*y
= e^(lim  ---------------)   =   e^0   =   1
     y→0  1 + (c)*(y^2)






: 這種題目要怎麼証壓
: 請高手解救   謝謝

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→ ggyy340:體積那題  請高手解救啊...