MATHEMATICS 184 (Section 922) - TERM EXAM 1
NAME:
STUDENT ID NUMBER:
SIGNATURE:
INSTRUCTIONS: No notes or books are to be used. Calculators
are allowed. No credit will be given for the correct answer without
the (correct) accompanying work. Use the back of the pages if you
need extra space.
1. Consider the function
y=
−1
(x − 1)2
(a) State the definition of a continuous function.
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(b) Is this function continuous? Why or why not.
[2]
(c) On which intervals is this function continuous?
[2]
(d) What is the domain of this function?
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(e) What is the range of this function?
[2]
(f) Identify the asymptotes of this function.
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2.(a) The Banque Nationale du Zaire pays 100% nominal interest on deposits, compounded monthly. You invest 1 million zaire.
(The ”zaire” is the unit of currency of the Republic of Zaire.) How
much money do you have after one year?
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(b) How much money do you have after one year if you invest 1 million zaire with interest compounded daily? Hourly? Each minute?
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(c) Does this amount increase without bound as interest is compounded more and more often, or does it level off? If it levels off,
provide a close ”upper” estimate for the total after one year.
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3. Suppose that in 1998 the population of city A was 70,000, and
this population was increasing at a rate of 4% per year. Suppose
that in 1998 the population of city B was growing at a rate of 3%
per year and that in 2001 the population of city B was 40,000 more
than that of city A. What was the population of city B in 1998?
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4.(a) Find an equation for the inverse of the function
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f (x) = 3ex + 1
(b) Graph the function f (x) and its inverse f −1 (x) together on the
grid below.
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5. Let
f (x) = e3x−3
and
g(x) = 2ln(2x)
(a) What is the value of f (f (1))?
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(b) Find a formula for f (g(x)). Simplify your answer as much as
possible.
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(c) Find a formula for g(f (x)). Simplify your answer as much as
possible.
[3]
(d) What is the domain of g(f (x))?
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