题目

求极限 1,lim(x→∞）（sinx/x +100) 2,lim(x→∞）xtan1/x 3,lim(x→1）sin^2 (x-1)/x-1

提问时间：2020-11-14

答案

1,lim(x→∞)(sinx/x +100)=0+100=100
2,lim(x→∞) x tan(1/x) = lim(x→∞) tan(1/x)/(1/x)=lim(x→∞) (-1/x^2) sec²(1/x)/(-1/x²)
= lim(x→∞) sec²(1/x) = lim(x→∞) 1/cos²(1/x) = 1
3,lim(x→1) sin^2 (x-1)/(x-1) = lim(x→1) sin (x-1) * lim(x→1) sin (x-1)/(x-1)
= 0 * 1 = 0