UNIVERSITY OF SARGODHA, SARGODHA BS 1st Term Examination 2015 Subject: BSCS Time Allowed: 2:30 Hours
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Paper text
UNIVERSITY OF SARGODHA, SARGODHA
BS 1st Term Examination 2015
Subject: BSCS
Time Allowed: 2:30 Hours
MATH-2213 Paper: Calculus & Analytical Geometry
Max. Marks: 80
Note: Objective part is compulsory. Attempt all the questions on your Answer Book.
Obiective Part
Q. No. 1
Write short answer of the following questions each in 2-3 lines. (16*2=32)
/
1.
If a s1, then find the values of x
/ it. Evaluate lim sin
1.
P.g 11d $019
ili.
Find the domain and range of y= x-1
iv.
What is difference between odd and even functions?
V.
,
vi.
vil.
vili.
,
ix.
• X.
/ X1.
xii.
xiii.
/ Xiv.
/ xv.
XVi.
Differentiate y = (sin x + 05x)coseck with respect to x. 4 - 6, P 9 186
If y = sin(rx-2), then find dx 239) P.g
20)
Discuss the function f (*) = x' is either increasing or decreasing or not.
Find the derivative of cosx at * 7f.
Evaluate
5. cos xx.
Find the equation of tangent line at (0,b) with slope k
If f(x) = x, then find '(16).
Evaluate in e-15 P.g 48
Find |re dx.
Evaluate LIx/axP.9 353, 82 19
What do your meant by conics?
Subjective Part
Note: Attempt FOUR questions out of SIX questions.
(4*12=48)
Q. No. 2
Find an equation of the normal line to the parabola f(x) =x-5x+4 that is
parallel to the line x- 3y =
5.
Q. No. 3
Q. No. 4
State and prove the Mean Value Theorem.
Find local maxima, local minima and saddle point
1(x,y) =x-2xy+2y*-2x+2y+1.
Q. No. 5
Evaluate the integral j-
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Q. No. 6
Show that the function 1: → R defined by *) - -1, i i rational
is
continuous at x = ,.
Q. No. 7
If y = (sin "x), then prove that (1-27)y*- xy -2=0.
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