We writeĪs x approaches - 2 from the right, f(x) gets larger and larger without bound and there is no limit. This graph shows that as x approaches - 2 from the left, f(x) gets smaller and smaller without bound and there is no limit. In this example, the limit when x approaches 0 is equal to f(0) = 1. Note that the left and right hand limits are equal and we cvan write Note that the left hand limit and f(1) = 2 are equal. Note that the left and right hand limits and f(1) = 3 are all different. The graph below shows that as x approaches 1 from the left, y = f(x) approaches 2 and this can be written asĪs x approaches 1 from the right, y = f(x) approaches 4 and this can be written as We consider values of x approaching 0 from the left (x 0). In fact we may talk about the limit of f(x) as x approaches a even when f(a) is undefined.Įxample 2: Let g(x) = sin x / x and compute g(x) as x takes values closer to 0. NOTE: We are talking about the values that f(x) takes when x gets closer to 1 and not f(1). In both cases as x approaches 1, f(x) approaches 4. We first consider values of x approaching 1 from the left (x 1). Example 1: Let f(x) = 2 x + 2 and compute f(x) as x takes values closer to 1.

No limits 2 gameplay