Question

求极限lim(x→2）( x^2-3x+2)/(x^2-4)

请问能附上解答过程吗？

Answer 1

lim(x趋近于2)(ln(x^2-3)/(x^2-3x+2))
=lim(x趋近于2)(ln(x^2-4+1)/(x-2)(x-1)
=lim(x趋近于2)[ln(x^2-4+1)^(1/(x-2))]/(x-1)
=lim(x趋近于2)[ln(x^2-4+1)^(1/(x^2-4))*(x+2)]/(x-1)
lim(x趋近于2)[ln(x^2-4+1)^(1/(x^2-4))=e

lim(x趋近于2)(ln(x^2-3)/(x^2-3x+2))=e^4
请采纳答案，支持我一下。

Answer 2

等会，我手机上图

lim(x→2)(x²-3x+2)/(x²-4)
=lim(x→2)(x-1)(x-2)/(x+2)(x-2)
=lim(x→2)(x-1)/(x+2)
=(2-1)/(2+2)
=1/4

刚手机上传图片了，不知道怎么回事，电脑上没显示。

Answer 3

lim(x→2)(x^2-4)/(x^2-3x+2)
=lim(x→2)(x-2)(x+2)/[(x-1)(x-2)]
=lim(x→2)((x+2)/(x-1)
=4