Jason Starr
Fall 2005
18.01 Calculus
Due by 2:00pm sharp
Friday, Oct. 21, 2005
Problem Set 4
Late homework policy. Late work will be accepted only with a medical note or for another
Instituteapproved
18.01 Calculus
Due by 2:00pm sharp
Friday, Dec. 9, 2005
Jason Starr
Fall 2005
Solutions to Problem Set 8
Late homework policy. Late work will be accepted only with a medical note or for another
Instit
18.01 UNIT 2 REVIEW; Fall 2007
The central theme of Unit 2 is that knowledge of f (and sometimes f ) tells us something about
f itself. This is even true of our rst topic, approximation. For instance,
STUDY GUIDE TO CALCULUS
This Student Study Guide accompanies the textbook Calculus by Gilbert Strang. It is correlated
section by section with the essential points of the text. The Guide contains four
3.1 Linear Approximation
CHAPTER 3
3.1
(page 95)
APPLICATIONS OF DERIVATIVES
Linear Approximation
(page 95)
This section is built on one idea and one formula. The idea is t o use the tangent line as a
4.1 The Chain Rule
DERIVATIVES BY THE CHAIN RULE
CHAPTER 4
4.1
(page 158)
The Chain Rule
(page 158)
+
+
The function sin(3x 2) is 'composed' out of two functions. The inner function is u(x) = 32 2. Th
Jason Starr
Fall 2005
18.01 Calculus
Due by 2:00pm sharp
Friday, Sept. 16, 2005
Solutions to Problem Set 1
Part I/Part II
Part I(20 points)
(a) (2 points)
(b) (2 points)
(c) (2 points)
(d) (2 points)
Jason Starr
Fall 2005
18.01 Calculus
Due by 2:00pm sharp
Friday, Sept. 30, 2005
Solutions to Problem Set 2
Part I/Part II
Part I(20 points)
(a) (2 points)
(b) (2 points)
(c) (2 points)
(d) (2 points)
2.1 The Derivative of a Function
CHAPTER 2
2.1
(page 49)
DERIVATIVES
The Derivative of a Function
(page 49)
In this section you are mainly concerned with learning the meaning of the derivative, and al
18.01 Practice Exam 2
Problem 1. (20)
Find the local maxima and minima and points of inection of
2x3 + 3x2 12x + 1 .
Then use this data to sketch its graph on the given axes, showing also where it is
Problem 1. (10 pts.) Find the tangent line to y =
1 2
x at x = 1
3
Problem 2. Find the derivative of the following functions:
a. (7 pts.)
x
1 x
b. (8 pts).
cos (2 x)
x
c. (5 pts). e 2 f ( x ) = g(x)
d
18.01 Calculus
Due by 2:00pm sharp
Friday, Dec. 2, 2005
Jason Starr
Fall 2005
Solutions to Problem Set 7
Late homework policy. Late work will be accepted only with a medical note or for another
Instit
18.01 Practice Questions for Exam 1
Solutions will be posted on the 18.01 website.
No books, notes, or calculators will be allowed at the exam.
1.
Evaluate each of the following, simplifying where pos
18.01 Exam 2
Tuesday, Oct. 17, 2006
Problem 1. (15 pts.) Estimate the following to two decimal places (show work)
a. (8 pts.)
b. (7 pts.)
sin( + 1/100)
101
Problem 2. (20 pts.) Sketch the graph of
y=
18.01 Practice Questions for Exam 1
Solutions will be posted on the 18.01 website
Problem 1. Evaluate each of the following:
a)
b)
d
x
dx 1 + 2x
x=1
d
(u ln 2u)
du
Problem 2.
(simplify your answer)
a)
18.01 Calculus
Due by 2:00pm sharp
Friday, Nov. 18, 2005
Jason Starr
Fall 2005
Solutions to Problem Set 6
Late homework policy. Late work will be accepted only with a medical note or for another
Insti
18.01 Practice Questions for Exam 2
Solutions will be posted on the 18.01 website. No books, notes, calculators. Show work.
1. For the function 3x5 5x3 + 1, sketch the graph over a suitable interval s
18.01 Fall 2006
Exam 1 Review
General Di erentiation Formulas
(u + v)0
=
u0 + v 0
(cu)0
=
cu0
(uv)0
u 0
v
=
u0 v + uv 0 (product rule)
u0 v uv 0
(quotient rule)
v2
d
f (u(x)
dx
=
=
f 0 (u(x) u0 (x) (
18.01 Calculus
Due by 2:00pm sharp
Friday, Nov. 4, 2005
Jason Starr
Fall 2005
Solutions to Problem Set 5
Late homework policy. Late work will be accepted only with a medical note or for another
Instit
Jason Starr
Fall 2005
18.01 Calculus
Due by 2:00pm sharp
Friday, Oct. 14, 2005
Solutions to Problem Set 3
Part I/Part II
Part I(20 points)
(a)(2 points)
(b)(2 points)
(c)(2 points)
(d)(2 points)
(e)(2