104/184 Quiz 1 Practice
End of week 2
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Very short answer questions
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes.
2x
1
(a) Solve
=2
7
Answer:
p
(b) Compute lim
q→3
q3 − 2
q2 + 1
Answer:
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
(a) Given that log2 x = 6, log2 y = 2.5, and log2 z = 0.5, find the value of logx
Answer:
x2 − 5x + 6
x→3 2x2 − 4x − 6
(b) Compute the limit lim
Answer:
√
yz.
Long answer question — you must show your work
3. 4 marks A publisher sells 5,000 copies a month the textbook “Calculus Is Fun” at the price
of $80 each. For each $5 decrease in price, she can sell 100 more copies per month. This
textbook costs $15,000 per month to maintain (ads, sales rep. etc) and each book costs an
additional $30 (to print and pay the author).
Note: in this problem you are ONLY setting up the equations. You do NOT have to solve for
break even values or any optimal production values.
(a) Find the linear demand equation for the textbooks. Use the notation p for the unit price
and q for the monthly demand.
Answer:
(b) Find the cost function, C = C(q), for producing q textbooks per month.
Answer:
(c) Find the monthly revenue function, R = R(q).
Answer:
(d) Find the monthly profit (or Net Income) function P (q).
Answer: