as2 - 1| . Then show that if x N 1 where you can choose...

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ECON 331 Written Assignment 2 due in class Sept. 30 1. .(a) $12 to be received 3 years from now has a present value of $10.97 when an annual interest rate of 3% is used. How many times a year is interest being compounded? (b) What is the present value of a constant string of payments V which will be received in perpetuity in the future at the end of every second year. That is the first payment is at the end of year T 2, the second is at the end of year T 4, the thiird is at the end of year T 6 and so on forever into the future. Use annual discounting at an interest rate of r in doing this question. 2.(a) Show that the following limit is equal to 6 lim x 1 x 2 3 x 4 by showing that when | x 1 | | x 1| is small | x 2 3 x 4 6 | is also small in the sense of being less than k | x 1| where k is a constant. (Hint: Show that | x 2 3 x 4 6 | | z x 1 | | z || x
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Unformatted text preview: 1| . Then show that if x N 1 where you can choose your own , | z | has a maximum value on this neighbourhood.) (b) Show that the following limit does not exist by showing that the expression takes on different values for x and x . lim x x | x | x (c) Evaluate the following limit by simplifying the expression to an expression whose limit you know. lim x 1 x 2 x x 2 3 x 4 Also evaluate this limit as x . 3.(a) Where are the discontinuities of the following function? Explain your answers. f x x 1 x 2 1 when x 2 1 f x when x 2 1 (b) What number a will make the following function continuous? f x 5 x 1 when x 2 f x ax 2 1 when x 2...
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