AMATHS ~急~

Please refer to the following solution:

圖片參考：http://hk.geocities.com/stevieg_1023/AMA3.gif

lim (√(x^2 2x) x)
x-) -∞
= lim (√(x^2 2x) x)/x
x-) -∞
= lim (√(x^2 2x)/x x/x)
x-) -∞
= lim (√(x^2/x^2 2x/x^2) x/x)
x-) -∞
= lim (√(1 2/x) 1)
x-) -∞
= - √(1 0) 1 (--Because -∞ sub into x which is insde √, So the answer insde √ must be (-)
= -1 1
= 0

2008-05-07 22:04:24 補充：
lim (√(x^2+2x)+x)
x-> -∞
= lim (√(x^2+2x)+x)/x
x-> -∞
= lim (√(x^2+2x)/x+x/x)
x-> -∞
= lim (√(x^2/x^2+2x/x^2)+x/x)
x-> -∞
= lim (√(1+2/x)+1)
x-> -∞
= - √(1+0)+1 <--Because -∞ sub into x which is insde √, So the answer insde √ must be (-)
= -1+1
= 0