此题极限怎么求?求详解,
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此题极限怎么求?求详解,
此题极限怎么求?求详解,
此题极限怎么求?求详解,
lim[x-->∞]x[√(x^2+2x+5)-(x+1)]
=lim[x-->∞]x[√(x^2+2x+5)-(x+1)]*[√(x^2+2x+5)+(x+1)]/[√(x^2+2x+5)+(x+1)]
=4lim[x-->∞]x/[√(x^2+2x+5)+(x+1)]
=4lim[x-->∞]1/[√(1+2/x+5/x^2)+(1+1/x)]
=4/2
=2