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 n
MATH 20502H
Quiz #1
Any answers which require logarithms to be expressed should be put in terms of natural or common logarithms. Show all work. 1. (3 points) If f (x) = 2x2 - 3x, simplify the expressi
MATH 20502H
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. (3 points) If f (x) = 2x2 - 3x, simplify th
MATH 20502H
Quiz #2
Name:
2x if
x3
a
if 3 < x < 8 continuous everywhere.
1. (4 pts) Find a and b to make the function f (x) =
x
4x + b if
x8
2. (6 pts) For each of the following limits, either determ
MATH 20502H
Quiz #2
Name:
2x if x3 a if 3 < x < 8 continuous everywhere. 1. (4 pts) Find a and b to make the function f (x) = x 4x + b if x8 Each of the individual parts of this function can be easil
MATH 20502H
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.
MATH 20502H
Quiz #3 Solutions
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 funct
MATH 20502H
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
MATH 20502H
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 comp
MATH 205-02H
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 follow
MATH 205-02H
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)
MATH 205-02H
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 b
MATH 205-02H
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 o