Upcoming SlideShare
×

# M1 Prsolutions08

2,370 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
2,370
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
5
0
Likes
0
Embeds 0
No embeds

No notes for slide

### M1 Prsolutions08

1. 1. 1. :-> 2. _ _ _ _ _ _ _ _ _ :->a 3. Change the order of integration in the integral :-> 4. Change the order of integration in the :-> 5. In polar coordinates the integral is :-> 6. In polar coordinates the integral :-> 7. :-> 8. :-> 9. Change the order of integration in the following integral :-> 10. Change the order of integration in the integral :- > 11. :-> 12. :->1 13. :->3 14. :-> 15. :->26 16. :-> 17. :-> 18. :->(e-1)3 19. Evaluate taken over the volume bounded by the planes x=0, x=1, y=0, y=1 and z=0, z=1. :-> 20. :->1 21. :->1
2. 2. www.prsolutions08.blogspot.com 22. _ _ _ _ _ _ _ _ _ _ _ :-> 23. :-> 24. _ _ _ _ _ _ _ _ _ _ _ :->9 25. _ _ _ _ _ _ _ _ _ _ _ :-> 26. By double integration, the area bying inside the circle r=asin θ and outside the cardioid r=a(1-cosθ) is :-> 27. By double integration, the area lying between the parabola y=4x-x2 and the line y=x is :- > 28. The area between the parabolas y2 =4ax and x2=4ay is :-> 29. The area bounded by the curves and is :-> 30. The surface area of the solid generated by the revolution about y-axis , of the arc of the curve x=f(y) from y=a to y=b is :-> 31. The surface area of the solid generated by the revolution about x-axis , of the arc of the curve y=f(x) from x=a to x=b is :-> 32. The volume of the solid generated by the revalution of the area bounded by the curve r=f(θ) and the radii vectors , , about the line θ= is :-> 33. The volume of the solid generated by revolution of the area bounded by the curve r=f(θ), and the radii vectors , , about the initial line θ =0 is :-> 34. The volume of the solid generated by revolution about the y-axis , of the area bounded by the curve x=f(y), the y-axis and the abscissac y=a, y=b is :-> 35. The volume of the solid generated by revolution about the x-axis , of the area bounded by the curve y=f(x), the x-axis and the ordinates x=a, x=b is :-> 36. The length of the curve r=asin θ between θ =0 and is :->πa 37. The length of the arc x=t, y=t from t=0 to t=4 is :->4 38. The length of the arc of the catenary y=c cosh from x=0 to x=a is given by :- > 39. The length of the arc of the curve x=acosθ, y=a sinθ from θ=0 to is :->
3. 3. www.prsolutions08.blogspot.com 40. The length of the arc of the curve θ=f(r) between the points where r=a and r=b, is :->L= 41. The length of the arc of the curve r=f(θ) between the points where and , is :- >L= 42. The length of the arc of the curve x=f(t), y=g(t) between the points where t=a and t=b is :- >L= 43. The length of the are of the curve x=f(y) between the points where y=a and y=b is :->L= 44. The length of the arc of the curve y=f(x) between the points where x=a and x=b is :- > 45. The length of the curve x=et cost from t=oto t=π/2 is :-> 46. The length of the curve y=x from x=0 to x=4/3 is :-> 47. The arc of the upper half of the cardioid r=a(1+cos θ) is bisected at θ = _ _ _ _ _ _ _ _ _ _ _ _ _ :->π/2 48. The length of one arch of the cycloid x=a(t-sint), y=a(1-cost) is :->8a 49. The entire length of the cardioid r=a(1+cosθ) is :->8a 50. Where the curve x=a(θ+sin θ), y=a(1+cos θ) is symmetrical about :->y-axis 51. Where the curve x=a(θ+sin θ), y=a(1-cos θ) meet the x-axis? :->(0,0) 52. The curve x= a(t-sint) ; x=a(1-cost) is symmetrical about :->y-axis 53. If x=f(x) is odd and y=g(t) is even then the curve is symmetrical about :->y-axis 54. If x=f(t) is even and y=g(t) is odd then the curve is symmetrical about :->x-axis 55. The curve x=a (cost + log Tan ), y= a sin t is symmetrical about :->x-axis 56. Where the curve x=a(cost + log tan ), y=a sint meet the y-axis ? :->(0, ) 57. Where the curve x=acos y=b sin ) meet the y-axis ? :->(0, ) 58. The Asymptotes to the curve x=a[cos )], y= a sin θ is :->y=0 59. The Asymptotes to the curve x=a( ), y= a(1+cos θ) is :-> o asymptotes 60. The line θ=0 is tangent at the pole to the following ine of the curve :->r=a(1-cos θ) 61. The Tangents at the pole to the curve r=a(1+cos θ) is :->θ =π 62. The Tangents at origin to the curve r2=a2 cos 2 θ are :->θ = 63. The curve r=a(1+sin θ) is symmetrical about :->θ = π/2 64. If the equation of a curve does not change when θ is replaced by `-θ' then the curve is symmetrical about the _ _ _ _ _ :->initial line 65. The curve r2 = a2sin 2 θ is symmetrical about :->The pole and the line θ = 66. The curve r=acos2 θ, a 0 consists of _ _ _ _ _ _ _ _ _ _ loops :->4 67. The tangents at the pole to the curve r=a sin 3 θ are :->The Lines 68. The tangents at the pole to the curve r2=a2sin 2θ are :->θ = 0 and θ= 69. The equations of asymptotes to the curve r2=a2sec2θ are :->
4. 4. www.prsolutions08.blogspot.com 70. The curve 9 ay2 = (x-2a)(x-5a)2 is semmetrical about :->x-axis 71. The curve a2y2=x3(2a-x) is symmetrical about :->x-axis 72. Where the curve y(x2+4a2) = 8a3 meet y-axis? :->(0, 2a) 73. The tangents at the origin to the curve y2(a+x)=x2(3a-x) are :->y= 74. The curve y2(a+x) =x2(3a-x) is symmetrical about :->y-axis 75. The tangents at origin to the curve y2(x-a)=x2(x+a) are :->y= 76. The tangent at origin to the curve (x2+y2)=a2x is :->y= 77. The asymptotes to the curve a2y2=x3(2a-x) are :-> o asymptotes 78. The Asymptote to the curve xy2=a2(a-x) is :->x=0 79. The Asymptote to the curve y2(a+x)= x2(3a-x) is :->x+a=0 80. The curve x3 +y3 = 3 axy is symmetrical about _ _ _ _ _ _ _ _ _ :->The line y=x 81. The equation of the a symptote of the curve y2(2a-x) =x3 is _ _ _ _ _ _ _ _ _ _ :->x=2a 82. The Tangents at the Origin to the curve x2 y2 = a2(y2-x2) is _ _ _ _ _ _ _ _ _ _ :-> 83. For the curve ay2=x3 the origin is _ _ _ _ _ _ _ _ _ _ _ _ :->a cusp 84. The curve ay2 = x2 is symmetrical about _ _ _ _ _ _ _ _ _ _ :->The x-axis 85. The asymptote of the curve (a-x)y2 = x3 is _ _ _ _ _ _ _ _ _ _ :->x=a 86. The Equation of the oblique asymptote of the curve x3+y3 = 3 axy is :->x+y+a=0 87. The curve x3-y3 = 3 axy is symmetrical about _ _ _ _ _ _ _ _ _ _ :->The line y=-x 88. Find the points where the curve meets the x-axis :->x=0, x=-a 89. For the equation y2(a-x)=x2(a+x), the origin is _ _ _ _ _ _ _ :->a node 90. Envelope of y=mx+ is :->y2=8x 91. The envelope of the family of curves y=m2x+am is _ _ _ _ _ _ _ _ _ m being a parameter. :->a2+4xy=0 92. If a one parameter family of curves is given by A alpha2+Bα+C =0 then its envelope is :- >B2-4AC=0 93. The envelope of the family of straight lines x cosα+ ysin α = c sec α where α being a parameter, is _ _ _ _ _ _ _ _ _ :->a parabola 94. Envelope of the family of lines y=mx+a/m is _ _ _ _ _ _ :->y2=4ax 95. If the equation of a family of curves be a quadratic in parameter α, the envelope of the family is Discriminant _ _ _ _ _ _ _ _ _ _ _ :->=0 96. The Envelope of the familly of curves y= mx+ , is m being a parameter _ _ _ _ _ _ _ _ _ _ _ :-> 97. Radius of curvature y=4sinx-sin2x at x= is _ _ _ _ _ _ _ _ _ _ :-> 98. Evolute of a curve is the envelope of its _ _ _ _ _ _ _ _ _ :-> ormals 99. Envelope when f(x,y,α) is of the form A cos α+B sin α=C is where A,B,C are functions of x and y, and α is the parameter :->A2+B2=C2 100. The tangent at the origin to the curve y-x=x2+2xy+y2 is :->y=x 101. The tangent at the origin to the curve x4-y4+x3-y3+x2-y2+y=0 is :->x-axis 102. The coordinates of centre of curvature of the curve y=ex at (0,1) is _ _ _ _ _ _ _ _ :->(-2, 3)