Question

求极限 1.lim(x趋于正无穷)4x^2-3x+1/2x^2-6x+5

2.lim(x趋于正无穷) (2x-1/2x+1)^x+1
3.lim（x→1） sin（x-1）/x-1有详细过程，准确性高的，加分哦

Answer 1

1、
x→+∞
lim (4x^2-3x+1) / (2x^2-6x+5)
=lim (4x^2-3x+1)/x^2 / (2x^2-6x+5)/x^2
=lim (4-(3/x)+(1/x^2)) / (2-(6/x)+(5/x^2))
=(4-0+0) / (2-0+0)
=4/2
=2

2、
x→+∞
lim [(2x-1)/(2x+1)]^(x+1)
=lim [(2x+1-2)/(2x+1)]^(x+1)
=lim [1-2/(2x+1)]^(x+1)
=lim [1-2/(2x+1)]^[2(x+1)/2]
=lim [1-2/(2x+1)]^[(2x+1+1)/2]
=lim [1-2/(2x+1)]^[(2x+1)/2] * lim [1-2/(2x+1)]^[1/2]
=lim [1-2/(2x+1)]^[(2x+1)/2] * 1
=lim [1-2/(2x+1)]^[(2x+1)/-2 * -1]
=[lim [1-2/(2x+1)]^[(2x+1)/-2]]^(-1)
根据重要的极限：lim(x→∞) (1+1/x)^x=e
=e^(-1)

3、
x→1
lim sin(x-1) / (x-1)
换元：t=x-1
=lim(t→0) sint / t
根据重要的极限：lim sinx/x=1
=1

有不懂欢迎追问

Answer 2

1.lim(x趋于正无穷)(4x^2-3x+1)/(2x^2-6x+5)
=lim(x趋于正无穷)(4-3/x+1/x^2)/(2-6/x+5/x^2)
=4/2
=2

2.lim(x趋于正无穷) (2x-1/2x+1)^x+1
=lim(x趋于正无穷) (2x-0+1)^x+1
=lim(x趋于正无穷) (2x+1)^x+1
=+∞

3.lim（x→1） sin(x-1)/(x-1)
=lim(x→1)(x-1)/(x-1)
=1

Answer 3

0.0