Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech CSE/IT (Computer Science And Engineering/ Information Technology) 2020 March 1st Sem MA 1130 Enriched Calculus I Previous Question Paper
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Software Engineering) (Sem.?1)
ENRICHED CALCULUS-I
Subject Code : MA-1130
M.Code : 77255
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C. have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.
SECTION-A
1. Attempt the following :
a) Explain how the vertical line test is used to detect functions.
b) Graph the parabola f (x) = x
2
. Explain why the secant lines between the points
(?a, f (?a)) and (a, f (a)) have zero slope.
c) Evaluate lim ,
x a
x a
x a
?
?
?
a > 0.
d) Suppose
3 , 2
( )
2, 2
x b x
h x
x x
? ? ?
?
?
? ?
?
. Determine a value of the constant b for which
2
lim ( )
x
h x
?
exists and state the value of the limit, if possible.
e) Discuss the continuity of
1
sin , 0
( )
0 , 0
x x
f x x
x
?
?
?
?
?
?
?
?
at x = 0.
f) Use the definition of the derivative to determine ( )
d
x
dx
. Also find the equation of
the line tangent to the graph x at (4, 2).
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1 | M-77255 (S1)-2567
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Software Engineering) (Sem.?1)
ENRICHED CALCULUS-I
Subject Code : MA-1130
M.Code : 77255
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C. have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.
SECTION-A
1. Attempt the following :
a) Explain how the vertical line test is used to detect functions.
b) Graph the parabola f (x) = x
2
. Explain why the secant lines between the points
(?a, f (?a)) and (a, f (a)) have zero slope.
c) Evaluate lim ,
x a
x a
x a
?
?
?
a > 0.
d) Suppose
3 , 2
( )
2, 2
x b x
h x
x x
? ? ?
?
?
? ?
?
. Determine a value of the constant b for which
2
lim ( )
x
h x
?
exists and state the value of the limit, if possible.
e) Discuss the continuity of
1
sin , 0
( )
0 , 0
x x
f x x
x
?
?
?
?
?
?
?
?
at x = 0.
f) Use the definition of the derivative to determine ( )
d
x
dx
. Also find the equation of
the line tangent to the graph x at (4, 2).
2 | M-77255 (S1)-2567
g) Compute the derivative of
2 5
( 3 10)
5 1
x
x x e
x
? ?
?
.
h) Find y
/
(x), when sin xy = x
2
+ y.
i) State second derivative test for local extrema.
j) Suppose an airline policy states that all baggage must be box-shaped with a sum of
length, width and height not exceeding 64 in. What are the dimensions and volume of
a square-based box with the greatest volume under these conditions?
SECTION-B
2. a) Find the inverse of the function f (x) = x
2
+ 4 and write it in the form y = f
?1
(x). Also
verify the relationships f (f
?1
(x)) = x and f
?1
(f(x))= x.
b) Find the domain and range of the function f (x) = x
5
+ x .
3. a) Let
2 4 1
( )
1 1
x if x
f x
x if x
? ? ? ?
?
?
?
? ?
?
?
. Find the values of
1 1
lim ( ), lim ( )
x x
f x f x
? ?
? ?
, and
1
lim ( ),
x
f x
?
or state that they do not exist.
(b) Evaluate
sin
lim 5
x
x
x
? ?
? ?
?
? ?
? ?
.
4. a) A particle moves along the curve 6y = x
3
+ 2. Find the points on the curve at which
the y-coordinate is changing 8 times as fast as the x-coordinate.
b) Prove that the function
sin
0
( )
1 0
x
if x
f x x
x if x
?
?
?
?
?
?
? ?
?
is everywhere continuous.
5. a) Find the derivative of
sin cos
sin cos
x x
x x
?
?
.
b) Find the maximum value of 2x
3
? 24x + 107 in the interval [1, 3].
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1 | M-77255 (S1)-2567
Roll No. Total No. of Pages : 03
Total No. of Questions : 09
B.Tech. (Software Engineering) (Sem.?1)
ENRICHED CALCULUS-I
Subject Code : MA-1130
M.Code : 77255
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION - B & C. have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.
SECTION-A
1. Attempt the following :
a) Explain how the vertical line test is used to detect functions.
b) Graph the parabola f (x) = x
2
. Explain why the secant lines between the points
(?a, f (?a)) and (a, f (a)) have zero slope.
c) Evaluate lim ,
x a
x a
x a
?
?
?
a > 0.
d) Suppose
3 , 2
( )
2, 2
x b x
h x
x x
? ? ?
?
?
? ?
?
. Determine a value of the constant b for which
2
lim ( )
x
h x
?
exists and state the value of the limit, if possible.
e) Discuss the continuity of
1
sin , 0
( )
0 , 0
x x
f x x
x
?
?
?
?
?
?
?
?
at x = 0.
f) Use the definition of the derivative to determine ( )
d
x
dx
. Also find the equation of
the line tangent to the graph x at (4, 2).
2 | M-77255 (S1)-2567
g) Compute the derivative of
2 5
( 3 10)
5 1
x
x x e
x
? ?
?
.
h) Find y
/
(x), when sin xy = x
2
+ y.
i) State second derivative test for local extrema.
j) Suppose an airline policy states that all baggage must be box-shaped with a sum of
length, width and height not exceeding 64 in. What are the dimensions and volume of
a square-based box with the greatest volume under these conditions?
SECTION-B
2. a) Find the inverse of the function f (x) = x
2
+ 4 and write it in the form y = f
?1
(x). Also
verify the relationships f (f
?1
(x)) = x and f
?1
(f(x))= x.
b) Find the domain and range of the function f (x) = x
5
+ x .
3. a) Let
2 4 1
( )
1 1
x if x
f x
x if x
? ? ? ?
?
?
?
? ?
?
?
. Find the values of
1 1
lim ( ), lim ( )
x x
f x f x
? ?
? ?
, and
1
lim ( ),
x
f x
?
or state that they do not exist.
(b) Evaluate
sin
lim 5
x
x
x
? ?
? ?
?
? ?
? ?
.
4. a) A particle moves along the curve 6y = x
3
+ 2. Find the points on the curve at which
the y-coordinate is changing 8 times as fast as the x-coordinate.
b) Prove that the function
sin
0
( )
1 0
x
if x
f x x
x if x
?
?
?
?
?
?
? ?
?
is everywhere continuous.
5. a) Find the derivative of
sin cos
sin cos
x x
x x
?
?
.
b) Find the maximum value of 2x
3
? 24x + 107 in the interval [1, 3].
3 | M-77255 (S1)-2567
SECTION-C
6. a) If
3 4
2
( 1) 3 1
( )
4
x x
f x
x
? ?
?
?
. Find f
/
(x). (3)
b) A swimming pool is 50m long and 20m wide. Its depth decreases linearly along the
length from 3m to 1m. It is initially empty and is filled at the rate of 1m
3
/minute.
How fast is the water level rising 250 minutes after the filling begins? How long will
it take to fill the pool? (5)
7. An 8-foot-tall fence runs parallel to the side of a house 3 feet away. What is the length of
the shortest ladder that clears the fence and reaches the house? Assume that the vertical
wall of the house and the horizontal ground have infinite extent. (8)
8. a) Find the anti derivative of the function
4 2
4 6 x x x
x
? ?
. Check your answer by taking
derivative. (4)
b) If
3
0
sin 2 sin
lim
x
x a x
x
?
?
be finite, find the value of ?a? and the limit. (4)
9. Use the graphing guidelines to graph the function f (x)
3
2
10
1
x
x
?
?
. (8)
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 21 March 2020