Let f and g be defined in an open interval I, let a I, let...

Transcribed Image Text:

Let f and g be defined in an open interval I, let a € I, let n E N. Suppose f and g have derivatives up to order n. Suppose further that fe) and g) vanish at f(n) (a) a and nowhere else when <n and that lima exists. Show that f(x) lim xa g(x) = lim HI g(n) (x) Let f and g be defined in an open interval I, let a € I, let n E N. Suppose f and g have derivatives up to order n. Suppose further that fe) and g) vanish at f(n) (a) a and nowhere else when <n and that lima exists. Show that f(x) lim xa g(x) = lim HI g(n) (x)