University of Sargodha BS Term System, 15 Term Exam 2013 Subject: Computer Science Course: Calculus (MTH-tol)
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Paper text
University of Sargodha
BS Term System, 15 Term Exam 2013
Subject: Computer Science
Course: Calculus (MTH-tol)
Time Allowed: 2:30 Hours
Maximum Marks: 80
Note:
Section-T is compulsory. Attempt any four questions from section-ll. Attempt all
questions on your answer book.
• Section-l
Objective Part
Q1.
Write short answers of the following in two or three lines.
(16*2-32)
(1)
Evaluate lin let
Find the body's acceleration at the end points of the interval [0,2)
if the position of the body at any time i is s = 1-- 3tF2-
(11)
(iv)
(v).
(vii)
Evaluate the integral 1, la|do
com
Find slope of the curvey = at a = a.
Define continuity of a function at 3 - 2g-
Find the intervals in which the function /(a) = =°+
24 is
increasing.
(vil)
(viil)
(ix)
(x)
{xi)
Evaluate / = sin a° da.
Find 1 for a = tang.
I (/ (s) da = 10 and |
(a)da = T, then find /
(a) do.
Find critical points of the function / whose derivative is t
Find the average rate of change of J(i) = 2 + cost over the interval
(хії):
Define critical point of'a fuhction.
If y = tanu, 4=- and oe Insuthen fnd S
Find the equation of tangent to the curvey = es - 42+1 at the
(xv)
(xvi)
o. i
Evaluate Jo:
Evaluate I sec()do
Section-IL
(Subjective Part)
(a) Tiet.
dni.com
Q.3
Q.4
Q: 5
Q. 6
Q.T
= =1,
if a
53.
1(2) =
JEFT
if 2 > 3
Pind li /(e), Im. /(e) and lim /(o)
(b) Find the slope of the graph of y = a" + 1 at the point (2,5) and
use it to find the equation of the tangent line to y = 2°+1 at 2=2.
(a) Show that the function /(a) = (z| is not differentiable at q=0,
(b) Find - if y =
(a) At what points) is the tangent line to the curve y* = 22ª per-
pendicular to the line 40 - 3y +1 = 02-
(a) Find if a = sat
17001=38
(a) Find the local linear approximation of /(e) = Jim at to =
0.
(b) Evaluate the intreal wind rare site: stadni col
(a) Find the total area between the curve y
over: the interval (0,2).
(b) Find the volume of the solid that is obtained when the region
under thé curve v' i over the interval (1,
4) is revolved about the
z-axis.
(a) Let y = V4-4, -15 =
51. Find the area of the surface
generated by evolving the given eurve about z-axis.
(b) Find the exact length of the curve y = 3z8 from a =1 to z =
8.
6.