I came across this problem as shown in the title. Limit of sin(x)sin(1/x) as x approaches 0. I plot the graph using online graphing calculators and found that it is approaching zero. But can anybody please proof it? I am really stuck and don't know where to start.
Also I did try to search the internet and found that the limit of xsin(1/x) equals to zero as x approaches zero. I understand how that work. So my second question is can I say that limit of sin(x)sin(1/x) is the same as limit xsin(1/x) when x approaches zero, since limit of sin(x)/x equals 1 when x approaches zero?