KOC UNIVERSITY
MATH 106
FIRST EXAM
MARCH 26, 2012
Duration of Exam: 90 minutes
INSTRUCTIONS: No calculators may be used on the test. No questions, and talking allowed. You must always explain your ans
Midterm 1 2
Question 1. Let
_ 1 + sins: 2e"
f(m) m and g<x>=ex_1.
(a) Find the horizontal and vertical asymptotes of f (ac).
_ + X
Hommmqswea; x=ol m m 3 :00
= X 0 7\
\IUHLDA asdmy+fz.g EN" WoSQ
KOC UNIVERSITY
MATH 106 - CALCULUS I
Final Exam
January 9, 2012
Duration of Exam: 135 minutes
INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.
No books, no notes, no questions and no talking a
KOC UNIVERSITY
MATH 106 - CALCULUS I
Midterm II
December 14, 2011
Duration of Exam: 90 minutes
INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.
No books, no notes, no questions and no talking
KOC UNIVERSITY
MATH 106 - CALCULUS I
Midterm I
November 16, 2011
Duration of Exam: 90 minutes
INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.
No books, no notes, no questions and no talking a
KO UNIVERSITY
MATH 106
FIRST MIDTERM
MARCH 30,2011
Durat.ior of Exam: 100 mirutes
INSTRUCTIONS:
N o calculators
may be used on the test.
No books, no notes, no questions, and talking allowed.
You m
KOC UNIVERSITY
MATH 106
FINAL EXAM
MAY 26, 2012
Duration of Exam: 120 minutes
INSTRUCTIONS: No calculators may be used on the test. No questions, and talking
allowed. You must always explain your answ
KOC UNIVERSITY
MATH 106
SECOND EXAM
MAY 7, 2012
Duration of Exam: 105 minutes
INSTRUCTIONS: No calculators may be used on the test. No questions, and talking
allowed. You must always explain your answ
EALL 2M2 Mastmn Someons
QueStionl: )
An ambulance is moving fast along the emergency lane (emniyet seridi) on the E6 to deliver
an injured person to the hospital. For each 50 meters of distance that t
Math 201: Statistics . , January 12, 2007
Fall 2006 FINAL EXAM
Closed book & notes; with calculator, ow charts, and a formula sheet,2 hrs 15 mins.
Instructions: There are seven questions in this exam
Math 201: Statistics . November 10, 2011
KEY
Fall 2012, EXAM 1
100 Minutes
Instructions: There are six questions and one bonus question in this exam. Please inspect
the exam and make sure you have all
l. (20 points) > '
The probability that Melamet Ukor hit,
point range is 0.35, and om the free thr
, l<et from three-point range is 0,18,
line is 0.8
(a) (8 points) What is the probability that Me
Math 106: Calculus
Final - Fall 2010
Duration : 150 minutes
#1
#2
18
#5
12
#6
Signature
12
#4
Student ID
12
#3
Name
15
15
#7
8
#8
8
100
Put your name, student ID and signature in the space provided a
KOC
UNIVERSITY
MATH 106 - CALCULUS
Midterm II
April 9, 2007
Duration of Exam: 75 minutes
INSTRUCTIONS: Calculators may not be used on the test. No books, no notes, and
no talking allowed. You must al
Question 1: (15)
(a) Find the first four terms of the Taylor series generated by f ( x) = (1 x 2 ) 1 / 2 at x = 0 by
using the Taylor series generated by f ( x) = (1 + x) 1 / 2 at x = 0 .
(b) Find the
Math- 106, FALL 2005
Solutions to Final Exam Problems
1-a) Using the identity sin 2 =
/4
1
sin d =
2
/4
2
0
0
1
(1 cos 2 ) , we find
2
/4
1
1
(1 cos 2 ) d = sin 2
2
2
0
=
1 1 1
= .
2 4 2 8 4
1
b)
PART 1: 40 Minutes
Question 1: (10)
a) Find x such that 90 < x < 180 and cos(2x) = 0.8 if cos(37 o ) = 0.8
b) What is sin(2x) ?
Question 2: (10)
A continuous and differentiable function is described b
Question 1: (10 Points)
ln t
d
xe x dx
dt 2t 1
Find the following derivative :
Question 2: (10 Points)
Given that the derivative of e x ( x 2 2 x 1) is equal to e x ( x 2 3) , evaluate the
following i
Question 1: ( 10 Points)
Let f be a function which is thrice differentiable in the interval I. ( f ' , f ' , f ' exist) . Prove
that ( (c, f (c) is an inflection point for some c I if f ' (c) = 0 and
KOC
UNIVERSITY
MATH 106 - CALCULUS I
FINAL EXAM
January 14, 2009
Duration of Exam: 150 minutes
INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.
No books, no notes, no questions and no talking
10 November, 2005
1
Math 106 Exam # 1 Solutions
1.
2
2
sin 3 1
9 ( sin 3 )
= lim
= lim 9
a.
= 9.
0 2 cos
0 9 2 cos
0
3
cos
N
1
1
5x
5
b. Since lim
= xlim
= 5 , the line y = 5 is
Math 106
Exam 2 Solutions
1. Consider f (x) =
15 December, 2005
x2
.
x2 1
The domain of f is R \ cfw_1, 1.
Since lim f (x) = , lim+ f (x) = +,
x1
x1
x = 1 and x = 1 are vertical asymptotes.
lim f (x)
Question 1: (15)
1
Evaluate the integral
( ln( x)dx
0
Question 2: (15Points +5Points)
The continuous function f (x) has horizontal tangents at x = 2 , x = 1 and x = 3 . It has a
vertical tangent at x
Question 1: ( 10 Points)
Find all solutions to sin(2 x 1) = 0.2 for x [ , ] .
Question 2: ( 10Points)
Find the derivative of
x 2 + 1 using the definition of the derivative (which involves a limit)
Que
KOC
UNIVERSITY
MATH 106
FIRST MIDTERM
NOVEMBER 3, 2007
Duration of Exam: 120 minutes
INSTRUCTIONS: No calculators may be used on the test. No books, no notes,
no questions, and talking allowed. You m
KOC
UNIVERSITY
MATH 106 - CALCULUS
Final Exam
June 1, 2007
Duration of Exam: 135 minutes
INSTRUCTIONS: Calculators may not be used on the test. No books, no notes, and
no talking allowed. You must al
KOC
UNIVERSITY
MATH 106 - CALCULUS
Midterm III
May 9, 2007
Duration of Exam: 75 minutes
INSTRUCTIONS: Calculators may not be used on the test. No books, no notes, and
no talking allowed. You must alw
KOC
UNIVERSITY
MATH 106
SECOND MIDTERM
DECEMBER 8, 2007
Duration of Exam: 120 minutes
INSTRUCTIONS: No calculators may be used on the test. No books, no notes,
no questions, and talking allowed. You