Question

计算极限 ①limx→2﹙x²﹢5﹚／﹙x－3﹚②limx→+∞﹙2^x－1﹚／﹙4^x＋1﹚

Answer 1

1. limx->2(x²+5)/(x-3)=(2²+5)/(2-3)=-9

2.limx->+∞(2^x-1)/(4^x+1)=limx->+∞[(2^x-1)/2^x]/[(2^2x+1)/2^x]
=limx->+∞(1-1/2^x)/(2^x+1/2^x)
limx->+∞1/2^x=0
limx->+∞(2^x+1/2^x)=+∞
原式=0

Answer 2

①limx→2﹙x²﹢5﹚／﹙x－3﹚
=limx→2 ﹙x²-6x+9+6x-4﹚／﹙x－3﹚
=limx→2 [（x-3）²+6（x-3）+14]/(x-3)
=limx→2 [x-3+6+14/(x-3)]
=-1+6-14
=-9
②limx→+∞﹙2^x－1﹚／﹙4^x＋1﹚
=limx→+∞2^x／4^x
=limx→+∞1／2^x
=0

Answer 3

①limx→2﹙x²﹢5﹚／﹙x－3﹚
=（2²＋5）÷（2-3）
=-9

②limx→+∞﹙2^x－1﹚／﹙4^x＋1﹚
=limx→+∞﹙2^-x－4^-x﹚／﹙1＋1/4^x﹚
=[0-0]/[1＋0]
=0

Answer 4

①
lim(x→2)﹙x²﹢5﹚／﹙x－3﹚
=9/(-1)
=-9
②
lim(x->+∞)﹙2^x－1﹚／﹙4^x＋1﹚
= lim(x->+∞) ( 1/2^x -1/4^x) /( 1- 1/4^x)
=0