A compendium of quizzes MA 123F Fall 2010
Comments: Collected here are all the problems that appeared on your quizzes this
semester, listed in somewhat random order. The intention of the quizzes was to make sure
you were keeping up with the material, cons
Quiz 1 MA 123F
Tuesday, Sept. 14, 2010
(1) For this question, use the two graphs below. In each case (a)(d), determine whether
the limit exists, and if so determine its value. Justify your answer by listing the
limit laws and other facts you use.
Graph of
Quiz 2 MA 123F Tuesday, Sept. 21, 2010
Name:
Note: Question 2 is on the other side of this sheet.
(1) In each case (a)(c), determine whether the limit exists, and if so determine its
value. Show your work.
1
1
x1 x 1
x(x 1)
x+1
(b) lim +
x1
x+52
(a) lim
Quiz 3 MA 123F Tuesday, Sept. 28, 2010
Name:
(1) In each case (a)(b), determine the functions vertical and horizontal asymptotes.
Show your work.
2x2 + 1
(x 1)(x 3)
1
(b) f (x) = x +
(x 1)2
(a) f (x) =
(2) Let g (x) = x(x 1) and let
h(x) =
x + 1, if x 0
x
Quiz 4 MA 123F Tuesday, Oct. 5, 2010
Name:
Show your work.
(1) Let y =
5ex
. Find y and y .
x
(2) Let f (x) =
d
(3) Find
dx
d
(4) Find
dx
3
6 x
x
x
e
.
ex
. Find f (x) and f (0).
x)
(1 + e
x 3/2
.
ex
Quiz 5 MA 123F Tuesday, Oct. 26, 2010
Name:
Show your work.
(1) Find
d
(sin(x)2 + tan(x) .
dx
(3) If exy = 1, nd y at the point (2, 0).
(2) If cos(xy ) = x, nd y .
Quiz 6 MA 123F Tuesday, Nov. 2, 2010
Name:
Show your work.
(1) What is arcsin(1/2)?
(3) Let f (x) = arcsin(x3 + 1).
(a) What is the domain of f (x)?
(b) What is the range of f (x)?
(c) What is f (x)?
d
(2) Find
arccos(x) .
dx
Quiz 7 MA 123F Tuesday, Nov. 9, 2010
Name:
Show your work.
(1) Dierentiate log2
1+x
.
1x
2
(2) Dierentiate xx .
(3) Use the linear approximation of f (x) = ln(1 + 2x) at x = 0 to estimate ln(1.02).
Quiz 8 MA 123F Tuesday, Nov. 16, 2010
Name:
Show your work.
(1) The pictured tank is shaped like a cube of side 2 m. It is being lled with water at
a rate of 2 m3 /min. At what rate is the height of the water changing?
(2) Let f (x) =
x1
.
x2 + 3
(a) Find
Quiz 9 MA 123F Tuesday, Nov. 23, 2010
Name:
Show your work.
1. Find the local maxima and minima of f (x) = x2 x + 3 for x > 3.
2. In each case (a), (b) determine whether the limit exists, and if so, determine its
value. Show your work.
ln(1 + x) x
x0
x
(a
Final review MA 123F Fall 2010
Boston University
Contents
Preface
1. Limits and continuity
1.1. Computing limits
1.1.1. Plugging in: sum, product, quotient, and composition rules
1.1.2. Proving a limit doesnt exist
1.1.3. Indeterminate forms
1.1.4. Squeez