MATA32 Winter 2010
Quiz 6: Solutions
Name:
KEY
1. The picture below shows a graph of y = f (x). Does lim f (x) exist? If so, evaluate
x1
it; if not, explain why not.
3
2
1
4
3
2
1
1
1
2
3
2
3
As indicated in the picture, f (1) = 1. However, as x approac
Quiz 1: Solutions
Name:
KEY
1. A real-estate rm owns the upscale Parkvale Avenue Apartments, which consist of 100
apartments. At $700 per month, every apartment can be rented out. However, for each $50 per
month increase in rent, there will be 2 new vacan
MATA32 Winter 2010
Quiz 2: Solutions
Name:
KEY
1. The population of a town is currently 100,000. Suppose that the population grows
at the rate of 5% per year. Find the population 4 years from now.
After one year, the population will be 5% larger than it w
Midterm Solutions
1. First, from the denition, it is clear that f (x) is continuous for x = 5. Thus, the only
possible discontinuity is at x = 5. Note that lim f (x) = 15 + 2k 2 and lim f (x) =
+
x5
x5
27 + 2k. Therefore, for f (x) to be continuous at 5,
MATA32 Winter 2010
Quiz 3: Solutions
Name:
KEY
1
1. The demand equation for a product is p = 82 2 q . Express q in terms of p, using only
base 10 logarithms.
Take the logarithm (base 10) of both sides. We nd:
1
log p = log 82 2 q =
1
2 q log 8
2
1
= 2 log
MATA32 Winter 2010
Quiz 4: Solutions
Name:
KEY
1. A debt of $6,000 due ve years from now is instead to be paid off by three payments: $1000 now, $1500 in two years, and a nal payment at the end of four years.
What would this nal payment be if an interest
MATA32 Winter 2010
Quiz 9 Solutions
1. A manufacturer plans to fence in a 500 m2 rectangular storage area adjacent to a
building by using the building as one side of the enclosed area (see the picture below).
The fencing parallel to the building faces a h
MATA32 Winter 2010
Quiz 8 Solutions
Name:
1. Differentiate y =
KEY
ln x
.
x2
This is quotient rule: bottom times derivative of the top, minus
top times derivative of the bottom, over the bottom squared. In
this case:
x2
dy
=
dx
Continued on reverse.
1
x
MATA32 Winter 2010
Quiz 7 Solutions
Name:
KEY
1. Suppose the position function of an object moving along a number line is given by
s = f (t) = 2t3 7t + 1, where t is in seconds and s is in meters.
(a) Find the average velocity over the interval [2, 2.1].
MATA32 Winter 2010
Quiz 5: Solutions
Name:
KEY
1. Find the amount (future value) of an annuity consisting of payments of $150 at the
end of every six months for 4 years, at the rate of 8% compounded semiannually.
0
1
2
3
4
5
6
7
150(1.04)7
150(1.04)6
150