MATHS 101
Test 2
November 28, 2016
University of Bahrain
Department of Mathematics
MATHS101: Calculus I
Fall 2016
Test 2
ID:
Student’s Name:
Section:
Serial Number:
• Do not open the exam until you are instructed to do so.
• Show sufficient work to justify each answer.
• Calculators are allowed but cell phones are not allowed during the exam.
• Exchange of any material such as calculator, pen, eraser is not allowed.
• No questions are allowed.
• You have 1 hour to finish this exam. You can leave only after 30 minutes of the exam.
• There are 2 questions, one consists of 12 multiple choice questions and a total of 5 pages in this
exam.
• The multiple choice question should be filled in the bubble sheet and will be graded by the
computer.
Question Points Score
1
36
2
14
Total:
50
Exam Version: A
MATHS 101
Test 2, Page 2 of 5
November 28, 2016
Question 1 (36 points)
Choose the correct answer and shade the answer in the answer sheet for each of the following:
(1) If y
5x2 sin x
A. 10x
csc x, then y 1
cos x csc x cot x
D. 10x cos x csc2 x
(2) f pxq px9
(3) If f pxq B. 10x cos x csc x cot x
C. 5x cos x csc x cot x
E. 10x cos x
csc x cot x
F. 10x cos x cot2 x
6qex , then f 1 pxq A. p9x8 q ex
D. px8 q ex
px9
6qex
B. p9x8 q
px9
6qex
C. p9x8 q ex
px9
6q
E. p9x8 q
p x9
6q
F. p9x8 q ex
p x9
6qex
3x
, then f 1 pxq 1 x2
A.
x2 6x 3
p1 x2q2
B.
x2 6x 2
p1 x2q2
C.
x2 6x 4
p1 x2q2
D.
3x2 6x 1
p1 x2q2
E.
x2 6x 1
p1 x2q2
F.
x2 6x 1
p1 x2q
A. cospx6 q p6x5 q
B. sinpx6 q p6x5 q
C.
6x5
D. cospx6 q
E. cospx6 q p6x6 q
F. cospx6 q p6x5 q
(4) If y
sinpx6q, then y1 2
MATHS 101
(5) If y
Test 2, Page 3 of 5
x2
ex
sin 6, then y 1
A. 2x ex
D. 2x ex
(6) If y
tan x
November 28, 2016
sin 6
10x, then y 2
A. 2 sec2 x tan x
B. 2x
e x
E. 2x
ex
cos 6
C. 2x ex
F. 2x ex
10
D. 2 sec x tan x
(7) At which point on the curve y
B. sec2 x
C. 2 sec2 x tan2 x
E. 2 sec2 x tan x
F. 2 sec x
x2 6x
13, the slope of the normal line is equal to
A. p2, 5q
B. p5, 8q
C. p4, 4q
D. p4, 5q
E. p0, 13q
F. p4, 2q
(8) If y
A.
D.
log9p9x
p9x
px
1q, then y 1
9
1qpln 9q
1
1qpln 9q
cos 6
0.5?
B.
E.
9pln 9q
p9x 1q
p9x
1
1qpln 9q
C.
F.
3
1qpln 9q
p9x
p9x
9
1q
3
MATHS 101
Test 2, Page 4 of 5
x 10
|x 10|
(9) lim
x
Ñ10
A. 10
D.
November 28, 2016
B. 0
8
E.
4x2 5x
xÑ8 2x2
x
2
4
(10) lim
C. 1
10
F.
8
C.
2
A. 2
B. 4
D. 0
E.
8
F.
8
B.
?
1
x
2
C.
?
x
F.
?
x
A.
?
x
D.
?
x
(11) If y
?
x
1
2, then y 1
2 pln 2q
x2
1
2 pln 2q
x
x2
1
?
E. x
2 2
(12) The slope of the tangent line to the curve x3
A.
D.
3e2
e
3
B.
e
e
e
3
E. 3
e
e ey
2 pln 2q
1
2 pln 2q
x2
1 at p1, 1q is
C.
3
e
F.
e
3
4
MATHS 101
Test 2, Page 5 of 5
November 28, 2016
Question 2 (14 points)
(a) Using the definition of the derivative, find the derivative of the function
f pxq (b) Find the derivative of y
?
6x
psin xq2 ln x
5