Exercise 7.5 : Indeterminate Forms

EXERCISE 7.5

Evaluate the following limits, if necessary use l’Hôpital Rule :

12. If an initial amount A0 of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is A = A0 (1 + r/n)nt. If the interest is compounded continuously, (that is as n â†’ ∞), show that the amount after t years is A = A0en.

Answers:

(1) 1/2

(2) 2

(3) ∞

(4) 1

(5) 0

(6) 0

(7) -3/2

(8) 1

(9) e

(10) 1

(11) 1/√e