Let f(x) = |x| + 1 and g(x) = [x] - 1, where [.] is the greatest integer function. Let h(x) = f(x)/g(x). What is lim_{x→0-} h(x) + lim_{x→0+} h(x) equal to?

For x → 0-: x is slightly negative, [x] = -1, so g(x) = -1 - 1 = -2. f(x) = |x| + 1 → 1. So h(x) → 1/(-2) = -1/2. For x → 0+: x slightly positive, [x] = 0, so g(x) = 0 - 1 = -1. f(x) → 1. So h(x) → 1/(-1) = -1. Sum = -1/2 + (-1) = -3/2.