计算lim(x→∞)[√(1+x^2)-x]x
lim(x→∞)[√(1+x^2)-x]x （分子部分有理化）=lim(x→∞)[√(1+x^2)-x]x[√(1+x^2)+x]/[√(1+x^2)+x]=lim(x→∞)x/[√(1+x^2)+x]如果x→＋∞=1/2如果x→－∞=－∞
举一反三
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计算极限lim(x趋向于无穷大){[(a^x)+1]/x}^1/x,(a＞0,a不等于1)
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lim(x)lim(x→∞)[(x-1)/(x+1)]^2x
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【单选题】若 f ( x ) = ( x − 1 ) x 2 − 1 2 , g ( x ) = x − 1 x + 1 ,则? A. f ( x ) = g ( x ) "> f ( x ) = g ( x ) B. lim x → 1 f ( x ) = g ( x ) "> lim x → 1 f ( x ) = g ( x ) C. lim x → 1 f ( x ) = lim x → 1 g ( x ) "> lim x → 1 f ( x ) = lim x → 1 g ( x ) D. 以上等式均不成立
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