MA 113 Calculus I, Fall 2013
Written Assignment #2
Due Friday, September 13, 2013, at beginning of lecture
Instructions: The purpose of this assignment is to develop your ability to formulate and
communicate mathematical arguments. Your complete assignmen
MA 113 Calculus I Spring 2013
Written Assignment #2 Solution
Due Friday, February 1, 2013, at beginning of lecture
Question A: Let function f be dened by
x + 3
f (x) = x2
x2 + 2x + 2
for x 1,
for 1 < x 1,
for x > 1.
i) Compute the right- and left-hand li
MA 113 Calculus I, Fall 2013
Written Assignment #1
Due Friday, September 6, 2013, at beginning of lecture
Instructions: The purpose of this assignment is to develop your ability to formulate and
communicate mathematical arguments. Your complete assignment
MA 113 Calculus I, Fall 2013
Written Assignment #3
Due Wednesday, October 2, 2013, at beginning of lecture
Instructions: The purpose of this assignment is to develop your ability to formulate and
communicate mathematical arguments. Your complete assignmen
MA 113
Quiz 1
Name
Fall 2013
1. Suppose f (x) = x2 + 27x + 6 and g (x) = 3x Write (f g )(x) in the form
ax2 + bx + c and nd the roots of (f g )(x).
Solution:
(f g )(x) = f (g (x) = ( 3x)2 + 27( 3x) + 6 = 3x2 + 9x + 6
Then set (f g )(x) = 0 to nd the roots
MA 113 Calculus I, Fall 2013
Written Assignment #5
Due Wednesday, 30 October 2013, at beginning of lecture
Instructions: The purpose of this assignment is to develop your ability to formulate and
communicate mathematical arguments. Your complete assignmen
MA 113 Calculus I
Final Exam
Spring 2010
May 5, 2010
Answer all of the questions 1 - 7 and two of the questions 8 - 10. Please indicate which of
problem 8 - 10 is not to be graded by crossing through its number in the table below. Answer
as many extra cre
MA 113 Calculus I
Exam 3
Spring 2010
April 13, 2010
Answer all of the questions 1 - 7 and two of the questions 8 - 10. Please indicate which of
problem 8 - 10 is not to be graded by crossing through its number in the table below. Answer
as many extra cred
MA 113 Calculus I
Exam 2
Spring 2010
March 9, 2010
Answer all of the questions 1 - 7 and two of the questions 8 - 10. Please indicate which problem
is not to be graded by crossing through its number in the table below.
Additional sheets are available if n
MA 113 Calculus I
Exam 3
Spring 2010
April 13, 2010
Answer all of the questions 1 - 7 and two of the questions 8 - 10. Please indicate which of
problem 8 - 10 is not to be graded by crossing through its number in the table below. Answer
as many extra cred
MA 113 Calculus I
Exam 1
Spring 2010
February 9, 2010
Answer all of the questions 1 - 7 and two of the questions 8 - 10. Please indicate which problem
is not to be graded by crossing through its number in the table below.
Additional sheets are available i
MA 113
Quiz 3
Name
Fall 2013
1. Evaluate the following limits
(a)
1
lim x2 sin( )
x0
x
1
Hint: What is the range of sin( )?
x
Solution: Since 1 sin(1/x) 1, then x2 x2 sin(1/x) x2 . By the
Squeeze Theorem and
lim x2 = lim x2 = 0,
x>0
we have
x>0
1
lim x2 s
MA 113
Quiz 7 - October 31, 2013
Name:
1. Highly rigorous research has shown that the number of ghosts haunting the average
neighborhood on Halloween night between midnight and 5 a.m can be represented
by the function g (x) = 1 x4 2x3 + 4x2 + 5 (where x =
MA 113 Calculus I Spring 2013
Written Assignment #5 Solution
Question A: Compute dy/dx at the point P = (2, 1) on the curve y 3 + 3xy = 7 and show that the
1
5
linearization at P is L(x) = 3 x + 3 . Use L(x) to estimate the y-coordinate of the point on th
MA 113 Calculus I Spring 2013
Written Assignment #3
Due Friday, February 15, 2013, at beginning of lecture
Question A: If the function f is continuous on [2, 1] and f (2) = 1, f (0) = 2 and
f (1) = 0, is it possible that f is one-to-one?
If the answer is
MA 113 Calculus I Spring 2013
Written Assignment #4
Due Friday, March 1, 2013, at beginning of lecture
Question A:
Figure (A) shows f and gure (B) shows f . Sketch the graph of f and
explain your reasoning.
4
4
3
3
2
2
1
1
4 3 2 1
1
1
2
3
4
4 3 2 1
1
2
3
Question A: Let f (x) be the square of the distance from the point (2, 1) to a
point (x, 3x + 2) on the line y = 3x + 2. Find the minimum value of f (x).
Solution. The square of the distance from (x1 , y1 ) to (x2 , y2 ) is given by
d2 = (x2 x1 )2 + (y2 y
MA 113
Quiz 9 - November 14, 2013
Name:
1. Suppose f is a twice dierentiable function such that f (t) = t cos t,
f (0) = 2, and f (0) = 2. Find f (t). Then nd f (t).
Solution: f (t) is an antiderivative of f (t). Therefore,
f (t) =
t2
sin t + C
2
From th
MA 113
Quiz 4 - 3 October 2013
Name:Answer Key
Make sure to show all your work.
1. The equation of the tangent line to f (x) at x = 3 is y = 13(x + 29). Determine a, f (a),
and f (a).
Solution: We rst observe that a = 3. Then we note that f (a) = 13, beca
MA 113
Quiz 6 - October 17, 2013
Name: ANSWER KEY
1. Suppose that we have two variable resistors connected in parallel with resistances
R1 and R2 and measured in ohms (). The total resistance is given by
1
1
1
=
+
.
R(t)
R1 (t) R2 (t)
(a) Find R(0) if R1
MA 113
Quiz 8
Name
November 6th, 2013
1. Use LHpitals Rule to evaluate the limit, or state that LHpitals Rule does
o
o
not apply and explain why it does not. (2 points each)
(a)
sin(sin(sin(x)
x0
x2 1
lim
(b)
9x7 + 2x2 + 7
x1
x2 1
lim
Solutions:
(a)
sin(s
MA 113 Calculus I Exam 4
Fall 2009 December 15, 2009
Answer all of the questions 1 - 7 and two of the questions 8 - 10. Please indicate which problem is not to be graded by crossing through its number in the table below. Additional sheets are available if
MA 113 Calculus I Exam 3
Fall 2009 November 17, 2009
Answer all of the questions 1 - 7 and two of the questions 8 - 10. Please indicate which problem is not to be graded by crossing through its number in the table below. Additional sheets are available if