计算极限：limx趋向于无穷,[（5x^2+1）/(3x-1)]sin1/x

题目

计算极限：limx趋向于无穷,[（5x^2+1）/(3x-1)]sin1/x

答案

原式=(5x+1/x)/(3-1/x)*sin(1/x)
=(5+1/x²)/(3-1/x)*x*sin(1/x)
=(5+1/x²)/(3-1/x)*sin(1/x)/(1/x)
x→∞
1/x→0
所以sin(1/x)/(1/x)极限是1
所以原来极限=5/3