Question

求函数的极限

第40，38和第42题

Answer 1

方法如下图所示，

请认真查看，

祝学习愉快：

Answer 2

其实我也不知道
嘿嘿嘿这是初中的题吗
我初中数学最差😂😂😃😃

Answer 3

(40)
lim(x->π/3) (1-2cosx)/sin(x-π/3)
=lim(x->π/3) (1-2cosx)/(x-π/3) (0/0 分子分母分别求导)
=lim(x->π/3) 2sinx
=2(1/2)
=1
(42)
lim(x->∞) [(x^2+2)/(x^2-3) ]^[ (x^2+5)/2 ]
=lim(x->∞) [ 1+ 5/(x^2-3) ]^[ (x^2+5)/2 ]
=lim(x->∞) [ 1+ 5/(x^2-3) ]^[ x^2/2 ]
=lim(x->∞) [ 1+ 5/(x^2-3) ]^[ (x^2-3)/2 ]
= e^(5/2)

追问

求解一下第38题

追答

(38)
lim(x->∞) [(x+2a)/(x-a)]^x =8
lim(x->∞) [1 + 3a/(x-a)]^x =8
e^(3a) =8
3a = 3ln2
a=ln2

Answer 4

求函数的极限在无穷大