The University of British Columbia
9 October 2013
Alternate Midterm for All Sections of MATH 104 and
184
Time: 60 minutes
Signature
Student Number
MATH 104 or MATH 184 (Circle one) Section Number:
Special Instructions:
No memory aids are allowed. No calc
Math 104 Section 101 Quiz 3 Solutions
September 17, 2013
Each question is worth 2 points.
1. Let
x 2
f (x) = 1
2x
if x < 1
if 1 x 1
if x > 1
Is f continuous? If not, where is it discontinuous?
Solution. The three pieces of f are polynomial, hence everywhe
Math 104 Section 101 Quiz 2 Solutions
September 12, 2013
Each question is worth 2 points.
1. Let
x+1
x2
f (x) =
if x < 1
if x 1
Find
lim f (x)
lim f (x)
and
x1+
x1
Does f (x) have a limit as x 1?
Solution. As x 1 , f (x) = x + 1 1 + 1 = 2. As x 1+ , f (x)
Math 104 Section 101 Quiz 1 Solutions
September 10, 2013
Each question is worth 2 points.
1. Suppose a company can sell q widgets at price p, where q = 300 p/50.
Express p in terms of q.
Solution. We clear denominators to get 50q = 15000 p, or p = 15000 5
MATH 104
QL
Mocx MrornRru 2
3L October

201"1
 p.2 of.7
[10 marks]
p.m. ship A is 25 km due north of ship B. If ship A is sailing west at a rate of 16 km/h
and ship B is sailing south at 20 km/h, find the rate at which the distance between the two
ship
Math 104 Section 101 Quiz 5 Solutions
September 30, 2013
Each question is worth 2 points.
1. Find the derivative of
1
1 + x2
Where is the function dierentiable?
Solution. The denominator 1 + x2 is always positive, since x2 0, so we
never have division by
7 NOV
2013 Math 104/184
Page 2 of L1 pages
NRme:
Short Answer Questions. Each question is worth 3 points. Put your final answer
in the box provided, but NO CREDIT will be given for the a,nswer without the correct
[18] 1.
accompanying work.
(a) Find the eq
Math 104 Section 101 Quiz 14 Solutions
November 26, 2013
1. (4 points) Recall that the linear approximation of
a bound for the error.
17 is equal to 33/8. Find
Solution. We need to gure out what the maximum second derivative is between
a = 16 and x = 17.
Math 104 Section 101 Quiz 11 Solutions
November 4, 2013
1. Let y = x5 5x. Sketch the graph of the function, indicating x and yintercepts, extreme points, inection points, intervals of increase and decrease,
and concavity.
Solution. The domain of the func
Math 104 Section 101 Quiz 13 Solutions
November 20, 2013
Each question is worth 2 points.
In each of the following cases, use linear approximation.
1. Find an approximate value for
17.
Solution. Recall the formula f f (a)+f (a)(xa) when x is near a. We se
Math 104 Section 101 Quiz 11 Solutions
November 13, 2013
Each question is worth 5 points.
1. Find the dimensions of the square of maximum area bounded by the x and
yaxes and the parabola y = 3 x2 .
Solution. First, let x be the length of the square and
Math 104 Section 101 Quiz 7 Solutions
October 9, 2013
1. (2 points) Find the derivative of y = (ln x)2 .
Solution. We use the chain rule, with y = u2 , u = ln x, and obtain
dy du
1
2 ln x
dy
=
= 2u =
dx
du dx
x
x
2. (4 points) Find the derivative of y = x
Math 104 Section 101 Quiz 9 Solutions
October 22, 2013
Each question is worth 2 points.
1. Find
ex
x ln x
lim
Solution. As discussed in class, we have
lim
xinf ty
ln x
x
= lim x = 0
x
x e
e
Therefore,
ln x
=0
ex
We need to nd the reciprocal limit. Express
Math 104 Section 101 Quiz 10 Solutions
October 28, 2013
1. (4 points) Two people, A and B, move along a grid. A starts at (0, 0) and
moves up 1 unit per second. B starts at (0, 1) and moves right 1 unit per second.
a) After t seconds, what is the distance
Math 104 Section 101 Quiz 8 Solutions
October 17, 2013
Let q = p3/2 , where p denotes price and q denotes quantity demanded.
1. (1 point) What is the elasticity of demand?
Solution. Since elasticity equals the exponent of p in such an equation, = 3/2.
Alt
Math 104 Section 101 Quiz 4 Solutions
September 24, 2013
Each question is worth 2 points.
1. Given that f is continuous, nd a and b:
x2
if x < 1
f (x) = ax + b
if 1 x 1
0
if 1 < x
Solution. The three pieces of f are polynomial, hence everywhere continuous
Math 104 Section 101 Quiz 6 Solutions
October 3, 2013
Each question is worth 2 points.
1. Find the derivative of y =
x2 + x. Where is the function dierentiable?
Solution. First, the function is dened whenever x2 + x 0. We write x2 + x
as x(x + 1); the pol
Quiz  October 17
Write your name, student number, and answers on a blank sheet of paper. You can use the back of
the paper. No calculators, notes, or other aids.
(1) If $2000 is invested today at a 6% annual interest rate compounded continuously, how man
Double Quiz  Nov 28
Write your name, student number, and answers on a blank sheet of paper. You can use the back of the paper. No
calculators, notes, or other aids.
(1) A 5foot high fence runs parallel to the side of a house at a distance of 4 feet. Fin
Quiz  Nov 7
Write your name, student number, and answers on a blank sheet of paper. You can use the back of
the paper. No calculators, notes, or other aids.
(1) f (x) =
x+2
x3
(a) Find the domain of f .
(b) Find any vertical asymptotes of f . Justify you