Suppose f(x), g(x), and h(x) are three functions, with lim f(x) / g(x) = M and lim f(x) + g(x) / h(x) = L.

xc9(x) x→C x→C

(i) If M ‡ -1, show that either lim f(x) / h(x) = ML / 1+M or the limit does not exist.

x→C

(ii) What can you say if M = -1?