作者ahongyeh (小叶子)
看板trans_math
标题Re: [微分] 极限
时间Tue Nov 13 10:49:18 2007
※ 引述《betray911015 (回头太难)》之铭言：
: 1 1 1
: l i m ---- ( ------ - ---)
: x→0^+ √x sinx x
1 1 1
lim --- (------ - ---)
x→0+ √x sinx x
x - sinx
----------
x‧sinx
= lim --------------
x→0+ √x
x - sinx
= lim --------------
x→0+ sinx‧x^(3/2)
L'R 1 - cosx
= lim --------------------------------
x→0+ cosx‧x^(3/2) + (3/2)sinx‧√x
L'R sinx
= lim -------------------------------------
x→0+ -sinx‧x^(3/2) + (3/4)sinx‧x^(-1/2)
1
= lim --------------------------
x→0+ -x^(3/2) + (3/4)x^(-1/2)
√x
= lim --------------
x→0+ -x^2 + (3/4)
= 0
--
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