Math1011
Spring 2001 Prelim
IIIA1
The size of a population, P, at time t (in years) is given by:
P (t )
10e t
Use a linear approximation to estimate the population at
t = 0.15 years. Show all of your work.
Math1011
Spring 2001 Prelim
A1
The size of a pop
Math 1110 (Spring 2009)
Solutions to Prelim 2 (03/26/2009)
1
Math1110 (Spring 2009)
Prelim 2  Solutions
Question 1. Please simplify the following expressions. There should be no logarithms,
exponentials, or trigonometric functions remaining in your nal a
Math1011
Fall 2009 Prelim
Consider the function f(x) =
IA1
1
lnx
.
What are the domain and range of the function f(x).
Write an equation for the inverse function f1 (x).
Math1011
Fall 2009 Prelim
A1
Consider the function f(x) =
1
lnx
.
What are the doma
Math1011
Fall 2009 Prelim
IB1
Please answer the following questions about the function f(x)
whose graph is shown in the figure below.
Is f(x) a onetoone function? Why or why not?
On what intervals between 5 and 5 is f(x) increasing?
For which values o
Math1011
Fall 2002 Prelim
If f (x )
=
IIA1
x + 1, find the slope of f(x) at the point (3,2).
(use the difference quotient / definition of the derivative)
Find an equation for the line tangent to f(x) at (3,2).
Math1011
Fall 2002 Prelim
If f (x )
=
x + 1,
FinalB1
Math1011
Fall 2003 Final
Sketch the graph of the function f, given the following information
General Information:
f(2) = 2
f(0) = 0
F is continuous except at x=3
lim
lim f ( x) = 0
x 3
x
lim+ +
lim f ( x) = 0
x 3
First Derivative
f(x) has cr
Math1011 Learning Strategies Center
Spring 2004 Final
FinalA1
The graph shows the velocity of a car over a 10second period.
Estimate the acceleration of the car at t = 2 seconds. Explain your
reasoning.
Find the average acceleration of the car over the
FinalC1
Math1011
Fall 2000/Spring 2003 Final
Find f'(x) where f (x ) =
Find the limit, if it exist:
x
lim
x 0
0 te
t
x2
dt
2x
0
t 2 cos(t +1t ) dt
3
C1
Math1011
Fall 2000/Spring 2003 Final
Find f'(x) where f (x ) =
2x
0
t 2 cos(t +1t ) dt
3
This looks l
Math1011
Spring 2002/2003 Final
Find the exact values of the following definite integrals.
4
x +1
1 x x
3
2
dx
x 2 , x < 1
f ( x) =
f ( x) dx where
x ,x 1
C9
C9
Math1011
Spring 2002/2003 Final
Find the exact values of the following definite integrals.
4
Math 1110
Name:
Prelim 2
Instructor:
26 March 2009
Section:
INSTRUCTIONS PLEASE READ THIS NOW
This test has 8 problems on 13 pages, worth a total of 100
points. Please carefully write all your nal answers on the
page they are posed. There are 2 extra bla
Math 1110 (Spring 2009)
Solutions to Prelim 3 (04/21/2009)
1
Math1110 (Spring 2009)
Prelim 3  Solutions
Question 1. (16 points) Short answer.
xa 1
, where a and b are positive numbers.
x1 xb 1
(a) (4 points) Please evaluate lim
sin(x)
.
x 1 cos(x)
(b) (4
Math1011
Section 3.11
Find the linearization of f (x )
10/31/2012
3
x at a
8
and use this to find the value of L(7.9)
Find the linearization of f (x )
sin(x ) at a
and use this to find the value of L(0.1)
0
Math1011
Section 3.11
1
Find the linearization
Math1011
Section 4.6
11/14/2012
A rectangular plot of farmland will be bounded on one
side by a river and on the other three sides by a singlestrand electric fence. With 800m of wire at your
disposal, what is the largest area you can enclose, and
what are
Math1011
Section 4.3
11/7/2012
Given f(x) = x3  12x + 1
Find the intervals on which is increasing or decreasing.
Find the local maximum and minimum values of .
Find the intervals of concavity and the inflection points.
Math1011
Section 4.3
1
Given f(x) =
Math1011  Learning Strategies Center
Various Prelims
IIB1
The equation x2 + xy + y 3 =
11 defines the following curve:
Find the equation of the tangent line at (1, 2).
Find
dy
dx
if x sin y + ye x =
1
Math1011
Various Prelims
B1
The equation x2 + xy + y
A9
Math1011
Fall 2005 Final
Sketch the graph of one function (x) below so that all of the
following are true:
a)
lim f (x ) 1, lim + f (x ) 1, f (3) 2
=
= =
x 3
x 3
b ) f is not differentiable at x 3 and x 2
= =
c) f '(x ) > 0 everywhere except at x =

B9
Math1011  Learning Strategies Center
Section 1.6
The function f(x) is graphed below:
4
3
2
1
0
4
3
2
1
0
1
2
1
2
3
4
What is the domain and range of the f(x)?
Is f(x) onetoone? Why?
Sketch f1(x) in the graph above.
What is the domain and ra
Math 1110
Name:
Prelim 3
Instructor:
21 April 2009
Section:
INSTRUCTIONS PLEASE READ THIS NOW
This test has 6 problems on 14 pages, worth a total of
100 points. Please carefully write all your nal answers
on the page they are posed. There are extra blank
Math1011
Section 5.3
11/28/2012
Given the graph of the odd function f(x)
Regions A & B are semicircles
Regions C & D are triangles
Regions E & F are unknown shape
Evaluate the integrals by interpreting in terms of area
2
0
f (x )dx
4
0
f (x )dx
5
5
If
f
Math1011
Section 3.10
10/17/2012
A man starts walking north at 4ft/sec from a point P.
five minutes later a woman starts walking south at
5ft/sec from a point 500 ft due east of P. At what
rate are the people moving apart 15 min after the
woman starts wal
Math1011
Section 4.6
11/14/2012
A rectangular plot of farmland will be bounded on one
side by a river and on the other three sides by a singlestrand electric fence. With 800m of wire at your
disposal, what is the largest area you can enclose, and
what are
11/13/2013
Math1011
Section 4.4
Find the intervals on whichf (x ) 10xe is increasing or
x
decreasing.
Find the local maximum and minimum values of .
Find the intervals of concavity and the inflection points.
From the information above, and f(0)=0, f(1)=
Math1011
Spring 2012
IIIB1
In this problem we study the function f (x ) 2x 3 9x 2 12x
Find all critical points of f and identify the intervals on which
the function f is increasing/decreasing.
Find all the inflection points of f and identify the interval
Math1011
Fall 2000/Spring 2003 Final
Find f'(x) where f (x ) =
Find the limit, if it exist:
x
lim
x 0
0 te
t
x2
dt
2x
0
FinalC1
t 2 cos(t +1t ) dt
3
Math1011
Fall 2000/Spring 2003 Final
Find f'(x) where f (x ) =
2x
0
C1
t 2 cos(t +1t ) dt
3
This looks l
Math1011
Fall 2007 Prelim
Let g be the function defined by the formula g (x )
IIIA1
x 2 x 1
x 2
.
Find the local extrema of g and the open intervals on which
the function is increasing and decreasing.
A1
Math1011
Fall 2007 Prelim
Let g be the function d
A9
Math1011
Fall 2005 Final
Sketch the graph of one function (x) below so that all of the
following are true:
a)
lim f (x ) 1, lim f (x ) 1, f (3) 2
x 3
x 3
b ) f is not differentiable at x 3 and x 2
c) f '(x ) 0 everywhere except at x 3 and x 2
d) lim
Math1011  Learning Strategies Center
Section 1.6
B9
The function f(x) is graphed below:
4
3
2
1
0
4
3
2
1
0
1
2
1
2
3
4
What is the domain and range of the f(x)?
Is f(x) onetoone? Why?
Sketch f1(x) in the graph above.
What is the domain and ra
Math1011
Section 4.1
11/6/2013
Use the graph to state the absolute and local maximum
and minimum values of the function on [ 0 , 7 ].
1
Math1011
Section 4.1
Use the graph to state the absolute and local maximum
and minimum values of the function on [ 0 ,
Math1011 Learning Strategies Center
Spring 2004 Final
FinalA1
The graph shows the velocity of a car over a 10second period.
Estimate the acceleration of the car at t = 2 seconds. Explain your
reasoning.
Find the average acceleration of the car over the