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 cle
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 s
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. Di
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 st
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 str
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 w
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 +
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 deter
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 b
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
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,
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: S
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). The
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
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,
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. Di