MATH15100-47 Second Midterm
Lecturer: Kun Gao
November 16, 2011
You have 55 minutes to complete 6 questions. Write down your solutions on the bluebook. Write
your scratch work on the scratch paper. Discussion, textbooks, notes and calculators are not
allo
Calculus 151, Section 43
Instructor: Chris Skalit
Second Hour Exam
Please attempt all questions and write your answers in the blanks provided. The use of
calculators, cellphones, notebooks, etc. is strictly prohibited. You have 50 minutes in total.
Good l
Calculus 151, Section 43
Instructor: Chris Skalit
First Hour Exam
Please attempt all questions and write your answers in the blanks provided. The use of
calculators, cellphones, notebooks, etc. is strictly prohibited. You have 50 minutes in total.
Good lu
Calculus 151, Section 43
Instructor: Chris Skalit
Final Examination
Please attempt all questions and write your answers in the blanks provided. The use of
calculators, cellphones, notebooks, etc. is strictly prohibited. You have two hours in total.
Good l
Calculus 151, Section 41
Instructor: Chris Skalit
First Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete o
Calculus 151, Section 41
Instructor: Chris Skalit
Quiz 2
Name:
1. (8 points) Using induction, prove that for all x = 1, 1 + x + x2 + + xn =
Solution: Our statement, P (n), reads For all x = 1, 1 + x + + xn =
xn+1 1
.
x1
xn+1 1
.
x1
x2 1
. By factoring the
Calculus 151, Section 41
Instructor: Chris Skalit
Quiz 1
Name:
1. (5 points) Determine the values, x, for which the following inequality is satised:
x2 2x + 1 > 9
Solution: Equivalently, we must determine the x for which
(x 4)(x + 2) = x2 2x 8 > 0
Looking
Calculus 151, Section 41
Instructor: Chris Skalit
Final Exam
You have two hours to complete this exam. The use of calculators, cellphones, notebooks, etc.
is strictly prohibited. Partial credit will be awarded for answers that are either incomplete
or sli
Calculus 151, Section 41
Instructor: Chris Skalit
Second Hour Exam
You have 50 minutes to complete the exam. The use of calculators, cellphones, notebooks,
etc. is strictly prohibited. Partial credit will be awarded for answers that are either incomplete
Calculus 151, Section 41
Instructor: Chris Skalit
Quiz 4
Name:
1. (3 points) Using the intermediate value theorem, prove that the polynomial, f (x) =
2x3 + 5x2 + 3x 4, has a root in the interval, (0, 1).
Solution: From direct computation, we see that f (0
Calculus 151, Section 41
Instructor: Chris Skalit
Quiz 8
Name:
1. Let f (x) be a function whose derivative is given by f (x) = x2 1
(a) (3 points) Where is f increasing/decreasing on (, )?
Solution: Since f (x) = (x 1)(x + 1), we see that its zeros occur
Calculus 151, Section 41
Instructor: Chris Skalit
Quiz 7
Name:
1. (2 points) Give a precise statement of the mean value theorem.
Solution: Let f be continuous on [a, b] and dierentiable on (a, b). Then there exists a
c (a, b) such that
(f (b) f (a)
f (c)
Calculus 151, Section 41
Instructor: Chris Skalit
Quiz 5
Name:
1. Compute the following derivatives
x2
d
(a) (2 points)
dx 1 x3
Solution: From the quotient rule, we have
d
dx
(b) (2 points)
x2
1 x3
d
dx
=
(x3 + 1)3
d
(x2 )(1
dx
d
x3 ) dx (1 x3 )x2
2x(1 x
Triangle Inequality:
|a-b| |a|-|b|
|a+b|a|+|b|
|a-b|a|+|b|
Given x, y > -, then x+y 2xy
2
x+y
definition of a limit: The limit of f(x) at c, lim f(x) x c exists and is equal to L, if:
For every > 0, there exists a > 0 such that if 0 < |x-c| < , then |f(x
MATH15100-47 First Midterm
Lecturer: Kun Gao
Octorber 21, 2011
You have 55 minutes to complete 7 questions. Write down your solutions on the bluebook. Separate the solutions from your scratch work clearly. Discussion, textbooks, notes and calculators
are
Sample Final Exam Questions
1. Differentiate with respect to x . Write your answers showing the
use of the appropriate techniques. Do not simplify.
1
a.
x 1066 + x 2 x2
b.
ex
c.
sin ( x )
5+ x 2
2. Differentiate, writing your answers as in problem 1.
3x
a