Question

当x趋向于0时,(1+sinx)＾1/sin2x的极限

当x趋向于0时,(1+sinx)＾1/sin2x的极限,要过程的哦

Answer 1

lim(x→0）(1+sinx)＾1/sin2x
=lim(x→0）(1+sinx)＾1/(2sinxcosx)
=lim(x→0）(1+sinx)＾1/(2sinx)
=lim(x→0）[(1+sinx)＾1/(sinx)]^(1/2)
=e^(1/2)

Answer 2

=lim(x-->0) (1+x)＾1/2x
令x=1/n,n-->∞
原式=lim(,n-->∞) (1+1/n)^n/2
=e^(1/2)