MATH 205-02H
Quiz #6 Solutions
1. (4 points) Using two steps of Newtons method with a starting value of x0 = 1, produce an
approximation x2 to a zero of the function f (x) = x3 x+1. Your answer need not be arithmetically
simplied.
Let us note that f (x) =
MATH 205-04
Quiz #6
Name:
1. (4 points) Using two steps of Newtons method with a starting value of x0 = 1, produce an
approximation x2 to a zero of the function f (x) = x3 x+1. Your answer need not be arithmetically
simplied.
2. (8 points) An open-topped
MATH 205-04
Quiz #5 Solutions
1. (4 points) Approximate the two following values with well-chosen linear approximations: 3 997. We consider the function f (x) = 3 x = x1/3 , whose derivative is f (x) = 1 x-2/3 . For x close 3 to 1000 (as 997 is), we can u
MATH 205-04
Quiz #5
Name:
1. (4 points) Approximate the two following values with well-chosen linear approximations: (a) 3 997.
(b) (3.04)4 .
2. (10 points) Let f (x) = 2 + 3x2 - x3 . Answer the following questions about this function. (a) (4 points) Wher
MATH 20504
Quiz #4 Solutions
1. (12 points) Compute the following derivatives:
dy
(a) (4 points) Given y = x2 esec x , nd dx .
This is a product rule stacked with a chain rule (since esec x is a composition). Let us preemptively assign u = sec x, so that
MATH 20504
Quiz #4
Name:
1. (8 points) Compute the following derivatives:
(a) (4 points) Given y = x2 esec x , nd
(b) (4 points) For f (t) = cos
(c) (4 points) Compute
d
d
et 2
arcsin t
dy
.
dx
, nd f (t).
sin ( + ln ).
2. (4 points) Given the equality x
MATH 20504
Quiz #3 Solutions
1. (6 points) Compute the following innite limits, or, if the limit is uncomputable, briey describe
(in symbols or words) the relevant long-term behavior of the function.
4x3 +6x2 2
.
3
x 2x 4x+5
(a) (2 points) lim
Using the h
MATH 20504
Quiz #3
Name:
1. (6 points) Compute the following infinite limits, or, if the limit is uncomputable, briefly describe (in symbols or words) the relevant long-term behavior of the function. (a) (2 points) lim
4x3 +6x2 -2 3 x- 2x -4x+5
(b) (2 poi
MATH 20504
Quiz #2
1. (6 pts) Below is the graph of a function f (x). For each of the six quantities listed to the right, either give its value or specifically state that it does not exist.
1 1
x-3
lim f (x) = 4, since f (x) as shown is continuous at x =
MATH 20504
Quiz #2
1. (6 pts) Below is the graph of a function f (x). For each of the six quantities listed to the right,
either give its value or specically state that it does not exist.
f (2)
lim f (x)
x3
lim f (x)
1
lim f (x)
x3
x2+
1
lim f (x)
lim f (
MATH 20504
Quiz #1 Solutions
Any answers which require logarithms to be expressed should be put in terms of natural or common
logarithms. Show all work.
1. (8 points) There are currently 5000 inhabitants of the luckless town of Dunwich, MA, and its
popula
MATH 20504
Quiz #1
Any answers which require logarithms to be expressed should be put in terms of natural or
common logarithms. Show all work.
1. (8 points) There are currently 5000 inhabitants of the luckless town of Dunwich, MA, and its
population decre
MATH 205
Practice Exam #3
Name:
This test is closed-book and closed-notes. No calculator is allowed for this test. For full credit
show all of your work (legibly!), unless otherwise specied. Algebraic and trigonometric simplication of answers is generally
MATH 20508
Practice Exam #2
Name:
This test is closed-book and closed-notes. No calculator is allowed for this test. For full credit show all of your work (legibly!), unless otherwise specified. Answers may include all arithmetic operations, trigonometric
MATH 205
Practice Exam #1 Solutions
1. (8 points) A sample of phlebotinum-75 decays over time, losing 23% of its mass per year. We have just obtained a 20-gram sample of this element. (a) (3 points) Create a function f (t) to describe the expected mass of
MATH 205
Practice Exam #1
Name:
This test is closed-book and closed-notes. No calculator is allowed for this test. When answering
the questions you are only allowed to use tools and techniques that we have discussed up to this
point, i.e. no advanced dier
MATH 205-04
Exam #3
Name:
No calculator is allowed for this test. For full credit show all of your work (legibly!), unless otherwise specified. Algebraic and trigonometric simplification of answers is generally unnecessary. 1. (14 points) Answer the follo
MATH 205-04
Exam #1 Solutions
1. (8 points) Evaluate the following limits; when a limit can not be evaluated, explicitly say so. (a) (2 points) lim 3t .
t-1
Since an exponential function with positive base is continuous throughout, we may use straightforw
MATH 205-04
Exam #1
This test is closed-book and closed-notes. No calculator is allowed for this test. For full credit show all of your work (legibly!), unless otherwise specified. For the purposes of this exam, all arithmetic results should be simplified