Question

求下图极限，过程？

Answer 1

(a)
lim √[(x²-5x+6)/(x²-4)]
x→2
=lim √[(x-2)(x-3)/(x+2)(x-2)]
x→2
=lim √[(x-3)/(x+2)]
x→2
=√[(2-3)/(2+2)]
=√(-¼)
-¼<0，算术平方根无意义，极限不存在。
(b)
lim [(lnx)³-8]/[(lnx)²-4]
x→e²
=lim (lnx -2)(ln²x+2lnx+4)/[(lnx +2)(lnx -2)]
x→e²
=lim (ln²x+2lnx+4)/(lnx +2)
x→e²
=[ln²(e²)+2ln(e²)+4)/[ln(e²) +2]
=(2²+2·2+4)/(2+2)
=12/4
=3