经济数学试题无穷大无穷小1）limxsin1／xx→∞2）limsin（x-1）/x-1x→1

Question

经济数学试题 无穷大 无穷小
1）lim xsin1／x
x→∞
2）lim sin（x-1）/x-1
x→1

Answer 1

lim(x→∞)（x*sin(1/x)）=lim(x→∞)(x*(1/x))=1
lim(x→1)(sin(x-1)/(x-1))=1
(这两题都用了同一个等价无穷小 lim(x→0)(sin(x)/x)=1