1) use l'Hopital's rule to show (1+r/k)^kà e^r , kà infinity
2) show that y(k)=(1+r/k)^k is an increasing function of k greater or equal to 1
3) let xi and yi are cash flows of two projects for i=0,1,2,....,n such that x0<y0 and summation from i=0 to i=n (xi) > summation from i=0 to i=n (yi). Let Px(d) and Py(d) denote the present values of these two projects when the discount factor is d.
meaning, x0 + x1*d + x2*d^2 + ....+ xn*d^n = y0 + y1*d^1 + y2*d^2 + ....+ yn*d^n
a) show that there is a value c>0 such that Px (c) = Py( c )
b) calculate 50/12 = d + d^2 + d^3 + d^4 + d^5
The expert examines L-Hopital's rule for functions.