Question

这些题的极限怎么求？

Answer 1

（1）原式=lim(x->0) (3x)/(5x)
=3/5
（2）原式=lim(x->0) x/tanx
=1
（3）原式=lim(x->0) (1-cosx)/(cosx*x^2)
=lim(x->0) [(1/2)*x^2]/(x^2)
=1/2
（4）原式=lim(x->0) x*sin(1/x)
=无穷小量*有界量
=0
（5）原式=lim(x->∞) [(1-1/x)^(-x)]^(-2)
=e^(-2)
（6）原式=lim(x->0) {(1+3tanx)^[1/(3tanx)]}^3
=e^3
（7）原式=lim(x->∞) {[1+1/(x+2)]^(x+2)}^[(x+3)/(x+2)]
=lim(x->∞) e^[(1+3/x)/(1+2/x)]
=e
（8）原式=lim(n->∞) {(1-2/n^2)^[-(n^2)/2]}^(-2/n)
=e^0
=1
（9）原式=lim(x->∞) [(3x^2+5)/(5x+3)]*(2/x)
=lim(x->∞) (6x^2+10)/(5x^2+3x)
=lim(x->∞) (6+10/x^2)/(5+3/x)
=6/5