Review problems for the Final
The Final will be Thursday, December 10, 8:30-11:30 AM in McConomy Auditorium
Most of the problems on this list have appeared on previous review lists. Areas between curves,
volumes of revolution, and related rates are the on
Math 120 Solutions to Homework #6 Problems from Pages 131-133 (Section 2.7) 26. The situation described on page 132 is illustrated below.
Winter 2009
100
L
!
x (t )
In this problem we are given the derivative x "( t ) = 8 feet per second. We are " asked t
Math 120
Winter 2009
Solutions to Homework #7
Problems from Pages 173-175 (Section 3.4)
2.
If we use P(t) to represent the number of bacteria after t hours. As the population
doubles every 20 minutes, P(t) will be an exponential function with P(0) = 60 an
Math 120 Solutions to Homework #10 Problems from Pages 232-236 (Section 4.5) 40.
Winter 2009
In this problem, we will let x represent the number of $10 price rises that the apartment manager makes. If the manager makes x rises, then the monthly rent, r(x)
Math 120 Solutions to Homework #9 Problems from Pages 232-236 (Section 4.5) 10.
Winter 2009
In this problem, we will make the assumption that the amount of material used to construct the box is directly related to the surface area of the box. Our objectiv
Questions for Quiz 8:
1. Determine the antiderivative of f (x) =
1
x
which passes through the point (1, 12).
2. Determine the antiderivative of g(x) = cos(x) which passes through the point (, 2).
3. Determine the antiderivative of g(t) =
1
which passes th
Questions for Quiz 6:
Four of these questions involve theorems. Some of these theorems, especially the Mean
Value Theorem and the Extreme Value Theorem, will come up later. Master them for the
long term, not just Tuesdays quiz.
1. Determine the derivative
Questions for Quiz 7:
1. Suppose that a dierentiable function f satises f (8) = 24 and |f (x)| 3. What is
the smallest value that f (2) can have?
2. Is it possible for a dierentiable function f to satisfy f (1) = 4, f (6) = 13 and
|f (x)| 2?
3. Show that
21-120 Dierential and Integral Calculus
Quiz questions for Fall 2014:
Questions for Quiz 2:
5
1. If sec() = , determine sin(2).
3
2. Determine the equation of the line through (2, 5) and perpendicular to the line
2x + y = 6, and express it in the form Ax
Math 120 Solutions to Homework #2 Problems from Pages 8-10 (Section 1.1) 46.
Winter 2009
The rectangle in question is shown below with length l and width w.
l
w
The perimeter of the rectangle is: P = 2l + 2w. On one hand, the area of the rectangle is give
Math 120 Solutions to Homework #1 Problems from Pages 8-10 (Section 1.1) 2.
Winter 2009
(a) Reading the y-values from the graph we can say that f(-4) = -2 and g(3) = 4. (b) The values of x at which f(x) = g(x) are the x-coordinates where the two graphs cr
Logarithmic differentiation: Section 3.3 nos. 49-54.
Go study! Do the review problems and read the book. There will be
office
hours today(Sunday) at 4:30 if you need help. And I listed some of the
things(non comprehensive) that people are still having pro
Department of Mathematical Sciences
CARNEGIE MELLON UNIVERSITY
21-120 Differential and Integral Calculus, 10 units, Fall, 2009
Instructor: Dr. Russ Walker, Wean Hall 6219, ext. 8-9657, [email protected]
Text: Stewart, Essential Calculus:Early Transcende
21-120 Assignment for 10/23:
!
1. Differentiate: f (x) = sin1 e2x
"
2. Differentiate: g(x) = sec(2x)tan(x)
3. Suppose that a differentiable function f satisfies |f " (x)| 3 and f (2) = 3. Then what
is the largest possible value for f (5)?
4. Draw the grap
Review for Test 1
Test 1 will be Wednesday, September 23.
Here are the objectives for the test:
Be able to differentiate functions involving algebraic and trigonometric functions
including implicit differentiation and compositions.
Evaluate limits or show
21-120 Test 2 will be Monday, October 26.
At 8:30 Section C will take the test in PH 125C. Sections A, B and D will take it in Wean
7500.
At 9:30 Section E will take the test in SH 214. Sections F, G and H will take it in Wean
7500.
Related rates: 2.7 no
Review questions for Test 3
Test 3 will on Wednesday, November 18
1. Applied Extrema: Remember that you should verify that your answer is a maximum or
minimum as required, and provide a statement of your conclusion.
Section 4.5 nos. 12, 16, 17, 20, 31, 4
Math 120
Winter 2009
Solutions to Homework #3
Problems from Pages 33-35 (Section 1.3)
6.
The graph of the function f(x) that was defined in pieces is shown below.
y
4
3
2
1
-4
-3
-2
-1
1
2
3
4
x
-1
-2
The places where the left-hand and right-hand limits w
Math 120 Solutions to Homework #4 Problems from Pages 80-83 (Section 2.1) 4.
Winter 2009
The slope of the tangent line is given by the derivative of y evaluated at the point x = 1. The calculation of this derivative is shown below.
Lim 2(#1+ h ) # 5(#1+ h
21-120 Dierential and Integral Calculus
Quiz questions for Fall 2014:
Questions for Quiz 3:
Factor out any common factors from your answers:
1. Determine the derivative: f (x) = (x2 + 4x + 2)6
2. Determine the derivative: g(x) =
x2
x+4
3. Determine the de