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MATH209 Midterm AND Solutions Winter 2022
Fundamental Mathematics II (Concordia University)
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MATH 209/4 all sections except EC:
—
Fundamental Mathematics II
Midterm - March 2022 (1h30min)
Only approved calculators are permitted.
MARKS
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[81/1./(a) Find $60
7
.
Find functions f (3:) and g(x) with the following
properties:
/(b)
[8]
,
(1)
_
game—0
,
[7]/ 2. Let g(a:) =
lim
[9(93
7
(c)
[6]
9
/4.
/
.
(In)
we)
—1
_
lag—(35‘?
.
Work out the following in detail:
t
[12]/ 37(a) If f(z) =
//(d)
.23.
_
33g -g<w>—0
+ t) — 906)]
t-—>O
/(b)
—
..
11)
+ 5, find f’(w). Do not simplify.
If g(:23) = (—3a:3 + 5)[ln(:123) + 5], find g’(a:). Do not simplify.
3
Find h’(:c) if Mr) = PET—1‘5???
~4zv28
Suggest a function f (m) if (O) = 0 and f’ (m) =
f
3.7:.
A bank stock triples in ten years. Find the associated
rate of growth if interest is
compounded continuously. What would have happened at a rate of one-half
percent
more?
5. The cost of making a: crates is given by the function C a:
= 7, 000 + 251:.
(a) Find the average cost per unit if 100 crates are produced.
(b) Find the marginal average cost when 100 crates are produced and
interpret the
results.
(0) Use (a)
[10]
/
and (b) to estimate the average cost per unit if 101 crates
are produced.
6. Find 27’ for a:
tbtl
10/7T wo mo or
.
= :I;(p)
defined implicitly by 1+plnac = we? and evaluate 93’ at (p, w)
p‘tth
= (O, 1).
0a 5 eave from the same om a t e same t'1me. O ne t rave l 8 nor a
miles per hours and the other travels west at 40 miles per hour. How fast is the distance
between the two motorboats changing after 3 hours?
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