Definition of Limit Let f be a function defined on an interval around r = c (not at x = c.) We define the limit of the function f(x) as r approaches c, written lim f(x) to I -+ C be the number L (if one exists) such that f(x) is as close to L as we want whenever x is sufficiently close to c (but x * c). If L exists, we write lim f (x) = L. (a) Sketch the graph of a function where we CAN approximate L as accurately as desired by choosing values for x sufficiently close to 5. (b) Sketch the graph of a function where we CANNOT approximate L as accurately as desired by choosing values for r sufficiently close to 5. Mark intervals on your graph corresponding to "as accurately as desired" and "sufficiently close" to make it painfully obvious that L cannot be approximated as accurately as desired