用极限的定义证明lim[x→∞](x^2)/(x^2+1)=1
用定义证明极限实际上是格式的写法,依样画葫芦就是: 证对任意ε>0,要使 |(x^2)/(x^2+1)-1|=1/(x^2+1)<1/|x|<ε,只需|x|>1/ε,取X=1/ε,则当x>X时,有 |(x^2)/(x^2+1)-1|<1/|x...
举一反三
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lim[sub]x→∞[/]x+sin2x/x-sin2x=() A: 2 B: 2/3 C: 0 D: 1
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高等数学求极限,求lim[1/e*(1+x)^(1/x)]^(1/x)【x趋于0】
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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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设f(x)是多项式,且lim(x→∞)[f(x)-x^3]/x^2=2,且lim(x→0)f(x)/x=1,求f(x)
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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)