In some cases, numerical investigations can be misleading. Plot (x) = cos /x. (a) Does exist? (b) Show, by evaluating (x) at x = 1/2,

In some cases, numerical investigations can be misleading. Plot ƒ(x) = cos π/x.

(a) Does  exist?

(b) Show, by evaluating ƒ(x) at x = ±1/2, ±1/4 , ±1/6, . . . , that you might be able to trick your friends into believing that the limit exists and is equal to L = 1.
(c) Which sequence of evaluations might trick them into believing that the limit is L = −1?

lim f(x) x0