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SIMON FRASER UNIVERSITY
MATH 157 Quiz 1
Section D
October 1, 2007
Time: 11:35 – 12:
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INSTRUCTIONS
- Do not open this booklet until told to do so.
- This exam has 4 questions on 4 pages excluding this cover page. Please check to make sure your exam is complete.
- Calculators are not allowed. No electronic devices may be within reach of a student.
- Write your full name, student number and SFU email ID on the cover page.
- Please read the questions carefully, and make sure you un- derstand what you are asked to do!
- Please write with a black or blue pen.
- Use the reverse side of the previous page if you need more room for your rough work.
- You may lose marks if your explanations are incom- plete, missing, or poorly presented.
- You may attempt the questions in any order.
- You must stop writing immediately when asked to do so!
Question Score
Total /
1. The following questions are True/False questions. No explanation is required for your
answer. You do have four choices for your answers:
- True, I am sure. 2. False, I am sure.
- True, I am guessing. 4. False, I am guessing. If you select ”I am sure” you get 4 points for a correct, 0 points for an incorrect answer. If you select ”I am guessing”, you earn 3 points for the correct answer, and 1 point for an incorrect one.
[4] (a) The graph of the exponential function y = ax^ rises as we move to the right, i.e., ax is an increasing function for a > 0.
[4] (b) For x > 0 we have ln(x^4 ) − ln(x^3 ) = ln(x).
[4] (c) Two logarithms with different bases a and b (a > 0 and b > 0 ) are related via
logb(x) =
loga(x) ln(a)
[4] (d) Let f (x) =
x^2 − 1 x − 1
, and g(x) = x + 1. Then the two functions f and g are the same, i.e., f (x) = g(x) for all x.
[4] (e) The intersection of the supply and demand curves is called the break-even point
Question I am sure I am sure I am guessing I am guessing TRUE FALSE TRUE FALSE
(a)
(b)
(c)
(d)
(e)
3. Limits
[5] (a) Find the following limit:
lim x→ 1
x^2 − 1 x^2 + x − 2
[5] (b) Find the following limit:
lim x→∞
x^2 − 1 x^2 + x − 2
SHOW YOUR WORK
4. Cost and revenue. A local Lower Mainland bicycle company manufactures a high-
performance mountain bike, the ”Exhilarator”. The cost of manufacturing 500 bicycles is $500,000, whereas it costs $900,000 to produce 1000 bicycles. Assume the cost function is linear. Wholesale price of the Exhilarator is $1200. We choose the following units for our equations: Cost and revenue in Dollars, quantity of bicycles in units of 1.
[2] (a) What is the fixed cost of the production of the ”Exhilarator”?
[2] (b) What is the marginal production cost?
[2] (c) What is the cost function?
[4] (d) What production quantity is the break-even point?
SHOW YOUR WORK
