Question

极限!(x+sinx)/(x+cosx)的极限是多少

Answer 1

【x->∞ 0≤|sinx/x|≤1/|x| --> 0 ,0≤|cosx/x|≤1/|x| --> 0 故:

sinx/x ,cosx/x 为无穷小量.】

lim(x->∞) (x+sinx)/(x+cosx)

=lim(x->∞) (1+ sinx/x)/(1+ cosx/x)

= (1+0)/(1+0)

= 1