40. The curves y= sin (x+ and y touch when x = 0. The values of a and b are: 1+x A. a=, b=1 B. a = V3, b=1+ V3 C.a-b-(1+v3) D. a = V3, b=(1+V3) (x-1)(x-5) are 41. The asymptotes of the curve whose equation is y = A. x = -1, x = -3, y = 1 B. x = -1,x = 3,y = -1 C.x 1,x = 5, y 1 D. x = -1,x 3,y 1 3x2+1 (x+1)(x-3) 42. The equations of the asymptotes to the curve y are 2x2+ x-3 3 A. - 1, B. x= 1. X = -1, y 1 C.
40. The curves y= sin (x+ and y touch when x = 0. The values of a and b are: 1+x A. a=, b=1 B. a = V3, b=1+ V3 C.a-b-(1+v3) D. a = V3, b=(1+V3) (x-1)(x-5) are 41. The asymptotes of the curve whose equation is y = A. x = -1, x = -3, y = 1 B. x = -1,x = 3,y = -1 C.x 1,x = 5, y 1 D. x = -1,x 3,y 1 3x2+1 (x+1)(x-3) 42. The equations of the asymptotes to the curve y are 2x2+ x-3 3 A. - 1, B. x= 1. X = -1, y 1 C.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Solve Q40, 41, 42 explaining detaiily each step
Transcribed Image Text:udy aid in Advanced level Mathematics..
31. Given that y = x-2x the approximate change in y when x inereases from 2 to 2.003 is: A.
0.01
B. 0.02
C. 3.24
D. 0.24
32. Given that y = 2x'+ I the approximate increase in x when y increases from 3 to 3.06 is: A.
0.01
B. 0.02
C. 3.24
D. 0.24
33. An error of 2% is made in measuring the side of a cube. The corresponding percentage error
in the volume of the cube is:
A. 2%
В. 3%
C. 5%
D. 6%
34. An error of 0.5% is made in measuring the radius of a disc. The approximate percentage error
this will cause in the area is
A. 5.0%
B. 1.0%
C. 0.05%
D. 0.25%
35. If air is leaking from a balloon at the rate of lem' s' the rate of decrease of the surface area
of the balloon when the radius is 3cm is:
A. em's' B. cm s C. 2em s' D. 3em s"
36. The equation of the tangent to the curve x - 2y = 8 at the point (4, 2) is
A. y x-4
37. The equation of the tangent to the curve defined by x 3t, y=- at the point with parameter
B. y x-2
C. y=-x-2
D. y = x + 2
is:
A. tx + y-6=0 B. x + ty-6t=0 C. x + ty-6t =0 D.tx-ty +3t-3= 0
38. The equation of the normal to the curve x + xy-5 0 at the point (1, 2) is
A. 2x – 3y + 4 = 0 B. 3x-2y +4 =0 C. 3x+ 2y - 7=0 D. 2x - 3y + 8 =0
39. x + 3y = 5 is normal to the curve y=x+ 5x + 6 at the point with coordinate
A. (-4,2)
B.(-1,-
c(-)
D. (-1.2)
40. The curves y sin (x+ and y=
a+bx
touch when x=0. The values of a and b are:
1+x
A. a=, b=1 B. a= V3, b=1 + V3
C. a =
D. a= v3, b =(1+ V3)
41. The asymptotes of the curve whose equation is y =
(x-1)(x-5)
are
(x+1)(x-3)
A.x = -1, x = -3, y = 1
C.x 1, x = 5, y 1 D. x = -1, x 3,y = 1
B. x = -1,x = 3,y -1
3x2+ 1
42. The equations of the asymptotes to the curve y =
are
2x24 x-3
A. - 1 B. x= 1. X= -1. y 1
C. x=-x-1, y=D. y =xx=1
3x
43. If f(x) =
then as x o the curve y = f(x) approaches the line
2x+1
A. y= 3 from above
B. y = 3 from below
47
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