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**Unformatted text preview: *** - 9 3 5 * A 2 A—2935 First Year B. Sc. (Sem. I) Examination
February / March — 2015
CCM-102 CS : Mathematics for Comp. Sc. - II
(Calculus - I) Time : Hours] [Total Marks : 70 Instructions :
(1) vital SQllEiGl .- f-‘uurilcutrﬂ [ﬂan-[i Grlaqél HQ MQEH xiv-141. seat NO: Fillup strictly the details of .- signs on your answer book.
Name of the Examination :
" F.Y. B.Sc. (SEM. 1) Name of the Subject : ‘- CCM-102 CS : MATHEMATICS FOR COMP. SC. - 2
tsubjectcode Nu rSeCtiOFI NO. (1,2......) ilEl (2) All questions are compulsory.
(3) Figures to the right indicate full marks. Student's Signature 1 Answer the following questions : 10 l
(1) If f(x)=(1+3x)x;x¢0 is continuous at x20 then f<o>= —.
(2) If y=sinx+cosx then find y4n. (3) Explain ONE ONE AND ONTO functions with
illustration. 2x
x2+1 1
(4) Evaluate i dx .
0 (5) The integral of cosx is sinx then the integral of cos (ax + b) = A-2935] 1 [ Contd... 1 x = x¢—— 2 (a) If f( ) 2x+1 2 then prove that 5 2X+1 3 x = ,x¢——_ 2X+3 2 OR (a) Show that f(x)=3x2+2x_1 is continuous at 2. 5
(b) Attempt any two : 10 (1) Define Domain and Range of the function and find x2—9 x—3 ' the same for f(x)= 1
(2) If f(x)=J; and g(x)=—2 then find the domains x of the fog and (3) If f(x)=5x—2; xeN If range of the function is {3,8,13} then find the Domain. —1
(4) If f is a real function defined by f (x)=% then
prove that f(2x)=m.
f (x)+3
3 (a) Obtain limeém 793 +892 +59—7. 5
OR
(a) Show that f (x)=sinx is continuous for every value 5 of x.
A-2935] 2 [ Contd... (a)
(b) (b) Attempt any two : 10
(1) Examine the continuity of the function defined by
—x2,xSO
5x—4,0<x<1
f(x)= 2
4x —3x,1<x<2
3x+4,x22
at the points 0, 1, 2.
1. x2—16
(2) Obtain 1m
H4 4x2 +9—5
1, Vx+3—Jg
- 1m —
(3) Obtain xﬁ3 x2_9
(4) Investigate the points of continuity and
discontinuity of the function f defined by
x2
——a,xSa
_ a
f(x)- 2
a
a——,x>a
x
Find the nth derivative of sin (ax+b). 5
OR
If y=10g<ax+b);a,b,xeR then find y”. 5
Attempt any two : 10
x2
. . .
(1) Obtain n derivative of —(x+2)(2x+3)
(2) Obtain the nth derivative of (ax+b)m.
_ x—l
(3) Obtain derivative of y — (x_2)(x_3)
(4) Obtain nth derivative of log (x+‘/1+x2) at y =0.
3 [ Contd... A-2935] 5 (a) Evaluate : Jlog(x+1)dx. 5 OR
IL
(a) Evaluate: x2(x4 +1)3/4 5
(b) Attempt any two : 10
dx
(1) Evaluate JW
(2) Find the area of the region bounded by the A-2935] (3) (4) parabola y2=4x and the line y=4x. I L
Evaluate Sin x(a+ b cos x) xdx Evaluate —.
J‘x4 — x2 +1 4 [ 100] ...

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