A-2935 - First Year B. Sc. (Sem. I) Examination February March - 2015 CCM-102 CS Mathematics for C

A-2935 - First Year B. Sc. (Sem. I) Examination February March - 2015 CCM-102 CS Mathematics for C

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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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