CONCORDIA UNIVERSITY Department of Mathematics and Statistics
Course Number Section(s)
MATH 209 A,AA B, C D,E, EC
Examination Date Time Pages
Final December 2022 3 hours 3
Instructors Course Examiner
I. Gorelyshev, H. Greenspan, I. Cojocaru
D. Pearce, F. Romanelli, C. Santana
Special Instructions:
e Ruled booklets to be used.
e Answer all questions. Justify and explain all your answers in order to obtain full credit.
e Only approved calculators are allowed.
1. (12 points)
(a) Find the following limit or explain why the limit does not exist.
tim 4z -z -5
z=-1322 + 5z + 2
(b) Find the following limit or explain why the limit does not exist.
M ~5z4 +322 - 222+ z + 1
T——00 22 + 3z + 2
(c) Find the following limit or explain why the limit does not exist.
4(z + 2)
im
-2 |z + 2|
2. (8 points) A particular person learns N items in ¢ hours, as given approximately by
N(it)=05Vt+3,t>0
Find the approximate change in the number of items learned when ¢ changes from 6 to 6.2 hours
by using differentials.
,Final Exam MATH 209 December 2022 Page 2 of 3
3. (9 points) Find the derivatives of the following functions. Do not simplify.
@ @)= (2t -195) (3 +e)
(v o) = s
(c) h(z)= [z*+In(32® + 1)]5
4. (8 points) The cost and revenue functions are
2
C(z) = 60z + 72000, R(z)= 200z — %,
where the production output in one week is * books. If production is increasing at a rate of 400
books per week when production output is 2000 books, find the rate of increase (decrease) in profit.
5. A company manufactures and sells z items per week. The weekly price-demand equation is
p+ 0.4z — 640 = 0.
(a) (10 points) Find all values of p for which demand is elastic and all values of p for which demand
is inelastic. If the current price is $500, and this price is increased, will revenue increase or decrease?
Explain.
(b) (7 points) Find the maximum weekly revenue, and the production level that will realize the
maximum revenue.
6. (13 points) Let f(z) = z(z — 1)3.
Sketch the graph of y = f(z) by using the graphing strategy. State all pertinent information.
, Final Exam MATH 209 December 2022 Page 3 of 3
7. (9 points) Find the following indefinite integrals.
(a)
/ (z’ + 2/ - -:—3) dz
(b)
S
2+e*
=T
(c)
8. (7 points) Calculate the following definite integrals.
(a) 2
/ V4 +z dz
0
(> - xr
./o (3 + 2z22)5 =
9. (8 points) Suppose that a country has Lorenz curve g(z) = z°.
Find the constant b such that the Gini index of income distribution for this Lorenz curve is 0.285.
10. (9 points) Calculate the area bounded by the graphs of the following two functions
f(z) = 2% — 16 and g(z) = z + 4 for —4 < z < 7. (accurate to three decimal places).
Course Number Section(s)
MATH 209 A,AA B, C D,E, EC
Examination Date Time Pages
Final December 2022 3 hours 3
Instructors Course Examiner
I. Gorelyshev, H. Greenspan, I. Cojocaru
D. Pearce, F. Romanelli, C. Santana
Special Instructions:
e Ruled booklets to be used.
e Answer all questions. Justify and explain all your answers in order to obtain full credit.
e Only approved calculators are allowed.
1. (12 points)
(a) Find the following limit or explain why the limit does not exist.
tim 4z -z -5
z=-1322 + 5z + 2
(b) Find the following limit or explain why the limit does not exist.
M ~5z4 +322 - 222+ z + 1
T——00 22 + 3z + 2
(c) Find the following limit or explain why the limit does not exist.
4(z + 2)
im
-2 |z + 2|
2. (8 points) A particular person learns N items in ¢ hours, as given approximately by
N(it)=05Vt+3,t>0
Find the approximate change in the number of items learned when ¢ changes from 6 to 6.2 hours
by using differentials.
,Final Exam MATH 209 December 2022 Page 2 of 3
3. (9 points) Find the derivatives of the following functions. Do not simplify.
@ @)= (2t -195) (3 +e)
(v o) = s
(c) h(z)= [z*+In(32® + 1)]5
4. (8 points) The cost and revenue functions are
2
C(z) = 60z + 72000, R(z)= 200z — %,
where the production output in one week is * books. If production is increasing at a rate of 400
books per week when production output is 2000 books, find the rate of increase (decrease) in profit.
5. A company manufactures and sells z items per week. The weekly price-demand equation is
p+ 0.4z — 640 = 0.
(a) (10 points) Find all values of p for which demand is elastic and all values of p for which demand
is inelastic. If the current price is $500, and this price is increased, will revenue increase or decrease?
Explain.
(b) (7 points) Find the maximum weekly revenue, and the production level that will realize the
maximum revenue.
6. (13 points) Let f(z) = z(z — 1)3.
Sketch the graph of y = f(z) by using the graphing strategy. State all pertinent information.
, Final Exam MATH 209 December 2022 Page 3 of 3
7. (9 points) Find the following indefinite integrals.
(a)
/ (z’ + 2/ - -:—3) dz
(b)
S
2+e*
=T
(c)
8. (7 points) Calculate the following definite integrals.
(a) 2
/ V4 +z dz
0
(> - xr
./o (3 + 2z22)5 =
9. (8 points) Suppose that a country has Lorenz curve g(z) = z°.
Find the constant b such that the Gini index of income distribution for this Lorenz curve is 0.285.
10. (9 points) Calculate the area bounded by the graphs of the following two functions
f(z) = 2% — 16 and g(z) = z + 4 for —4 < z < 7. (accurate to three decimal places).
