Let the function f(x) = sin[x], where [·] is the greatest integer function and g(x) = |x|. What is lim(x→0) {f(x) g(x)} equal to?

For x slightly greater than 0, [x] = 0, so f(x) = sin 0 = 0, and f(x)g(x) = 0. For x slightly less than 0, [x] = −1, so f(x) = sin(−1) = −sin 1, and f(x)g(x) = −sin 1 · |x| → 0 as x → 0. Both one-sided limits equal 0, so the limit is 0.