Question 1

Find the arc length of the curve x =   , y =   dx, 0 ≤ t ≤ ln(2).

Accepted Answer

The answer of Find the arc length of the curve...

Question 2

Find all the points of intersection of the curves r =   sin $\theta$ and   = cos 2$\theta$.

Accepted Answer

A)    ,   , (0,0) 
B)    ,   
C)    ,   , (0,0) 
D)    ,   
E)    ,   
A)    ,   , (0,0) 
B)    ,   
C)    ,   , (0,0) 
D)    ,   
E)    ,

Question 3

Find the area of the region bounded by the hypocycloid x = a   $\theta$
, y = a   $\theta$
.

Accepted Answer

A)   $\pi$   square units 
B)    $\pi$   square units 
C)    $\pi$   square units 
D)    $\pi$   square units 
E)  $\pi$   square units 
A)   $\pi$   square units 
B)    $\pi$   square units 
C)    $\pi$   square units 
D)    $\pi$   square units 
E)  $\pi$   square units

Question 4

Find the area bounded by the polar graph r = 4 cos($\theta$).

Accepted Answer

A)  $\pi$ square units 
B)  2$\pi$ square units 
C)  4$\pi$ square units 
D)  8$\pi$ square units 
E)    $\pi$ square units 
A)  $\pi$ square units 
B)  2$\pi$ square units 
C)  4$\pi$ square units 
D)  8$\pi$ square units 
E)    $\pi$ square units

Question 5

Find the area bounded by the larger loop of the curve r = 1 + 2 sin($\theta$).

Accepted Answer

A)  2$\pi$ -   square units 
B)  2$\pi$ +   square units 
C)  $\pi$ -   square units 
D)  $\pi$ +   square units 
E)    -   square units 
A)  2$\pi$ -   square units 
B)  2$\pi$ +   square units 
C)  $\pi$ -   square units 
D)  $\pi$ +   square units 
E)    -   square units

Question 6

Find the equation of the parabola passing through the point (2, 5), having vertex at the origin and axis of symmetry along the y-axis.

Accepted Answer

A)  5   = y 
B)  5   = 4y 
C)  4   = 5y 
D)  3   = 4y 
E)    = 3y 
A)  5   = y 
B)  5   = 4y 
C)  4   = 5y 
D)  3   = 4y 
E)    = 3y

Question 7

Find the area of the surface generated by rotating the astroid x = a   t, y = a   t about   .

Accepted Answer

A)    square units 
B)    square units 
C)    square units 
D)    square units 
E)    square units 
A)    square units 
B)    square units 
C)    square units 
D)    square units 
E)    square units

Question 8

If the equation f( $\theta$) = g($\theta$) has no solutions, then the polar curves   and   do not intersect.

Accepted Answer

A) True 
 B)False

Question 9

Find the area of the surface generated by rotating x = t - sin t, y = 1 - cos t where t    [0, 2 $\pi$] about the x-axis.

Accepted Answer

A)    square units 
B)    square units 
C)    square units 
D)    square units 
E)  64 $\pi$ square units 
A)    square units 
B)    square units 
C)    square units 
D)    square units 
E)  64 $\pi$ square units

Question 10

Find the area of the surface generated by rotating the lemniscate r2 = a2 cos(2$\theta$) about the line $\theta$ = 0.

Accepted Answer

A)  4 $\pi$   square units 
B)  2   $\pi$  square units 
C)  2 $\pi$  square units 
D)    $\pi$   square units 
E)  4   $\pi$   square units 
A)  4 $\pi$   square units 
B)  2   $\pi$  square units 
C)  2 $\pi$  square units 
D)    $\pi$   square units 
E)  4   $\pi$   square units

Question 11

The maximum distance of the Earth from the sun is 9.3 ×   kilometres. The minimum distance is   kilometres. The sun is at one focus of the elliptical orbit. Find the distance from the sun to the other focus.

Accepted Answer

A)  3.2 × 106 kilometres 
B)  4.8 × 106 kilometres 
C)  6.4 × 106 kilometres 
D)  1.6 × 106 kilometres 
E)  8.0 × 106 kilometres 
A)  3.2 × 106 kilometres 
B)  4.8 × 106 kilometres 
C)  6.4 × 106 kilometres 
D)  1.6 × 106 kilometres 
E)  8.0 × 106 kilometres

Question 12

Find the Cartesian equation of the straight line tangent to the plane curve given parametrically by the equations x(t) =   + 2t + 2, y(t) = 1 - 3   - 2   at the point on the curve where t = -1.

Accepted Answer

A)  x -3y -1 = 0 
B)  y =1 
C)  y = x + 1 
D)  3x -y -3 = 0 
E)  y = 3x -7 
A)  x -3y -1 = 0 
B)  y =1 
C)  y = x + 1 
D)  3x -y -3 = 0 
E)  y = 3x -7

Question 13

Find the centre, eccentricity, and foci of the ellipse   +   = 1.

Accepted Answer

A)  Centre (1, -3);   =   ; foci (1 ±   , -3) 
B)  Centre (-1, 3);   =   ; foci (-1 ±   , 3) 
C)  Centre (1, 3);   =   ; foci (1 ±   , 3) 
D)  Centre (-1, -3);   =   ; foci (-1 ±   , -3) 
E)  Centre (1, -3);   =   ; foci (1 ±   , -3) 
A)  Centre (1, -3);   =   ; foci (1 ±   , -3) 
B)  Centre (-1, 3);   =   ; foci (-1 ±   , 3) 
C)  Centre (1, 3);   =   ; foci (1 ±   , 3) 
D)  Centre (-1, -3);   =   ; foci (-1 ±   , -3) 
E)  Centre (1, -3);   =   ; foci (1 ±   , -3)

Question 14

Which of the following plane parametric curves is a parametrization of an ellipse centred at (4, -2)?

Accepted Answer

A)  x = 3 - 4cos(t), y = 5 + 2sin(t), 0 $\le$ t $\le$ 2$\pi$ 
B)  x = 3 + 4cos(t), y = 5 - 2sin(t), 0 $\le$ t $\le$ 2$\pi$ 
C)  x = 4 + 3cos(t), y = -2 + 5sin(t), 0 $\le$ t $\le$ 2$\pi$ 
D)  x = - 4 + 3cos(t), y = 2 + 5sin(t), 0 $\le$ t $\le$2$\pi$ 
E)  x = 4 - 2cos(t), y = 4 - 2sin(t), 0 $\le$ t $\le$ 2$\pi$ 
A)  x = 3 - 4cos(t), y = 5 + 2sin(t), 0 $\le$ t $\le$ 2$\pi$ 
B)  x = 3 + 4cos(t), y = 5 - 2sin(t), 0 $\le$ t $\le$ 2$\pi$ 
C)  x = 4 + 3cos(t), y = -2 + 5sin(t), 0 $\le$ t $\le$ 2$\pi$ 
D)  x = - 4 + 3cos(t), y = 2 + 5sin(t), 0 $\le$ t $\le$2$\pi$ 
E)  x = 4 - 2cos(t), y = 4 - 2sin(t), 0 $\le$ t $\le$ 2$\pi$

Find the arc length of the curve x = , y = dx, 0 ≤ t ≤ ln(2).

Find all the points of intersection of the curves r = $Find all the points of intersection of the curves r = sin \theta and = cos 2 \theta .$ sin $\theta$ and $Find all the points of intersection of the curves r = sin \theta and = cos 2 \theta .$ = cos 2 $\theta$ .

Find the area of the region bounded by the hypocycloid x = a $Find the area of the region bounded by the hypocycloid x = a \theta , y = a \theta .$ $\theta$ , y = a $Find the area of the region bounded by the hypocycloid x = a \theta , y = a \theta .$ $\theta$ .

Find the area bounded by the polar graph r = 4 cos( $\theta$ ).

Find the area bounded by the larger loop of the curve r = 1 + 2 sin( $\theta$ ).

Find the equation of the parabola passing through the point (2, 5), having vertex at the origin and axis of symmetry along the y-axis.

Find the area of the surface generated by rotating the astroid x = a t, y = a t about .

Find the area of the surface generated by rotating x = t - sin t, y = 1 - cos t where t $Find the area of the surface generated by rotating x = t - sin t, y = 1 - cos t where t [0, 2 \pi ] about the x-axis.$ [0, 2 $\pi$ ] about the x-axis.

Find the area of the surface generated by rotating the lemniscate r² = a² cos(2 $\theta$ ) about the line $\theta$ = 0.

The maximum distance of the Earth from the sun is 9.3 × kilometres. The minimum distance is kilometres. The sun is at one focus of the elliptical orbit. Find the distance from the sun to the other focus.

Find the Cartesian equation of the straight line tangent to the plane curve given parametrically by the equations x(t) = + 2t + 2, y(t) = 1 - 3 - 2 at the point on the curve where t = -1.

Find the centre, eccentricity, and foci of the ellipse + = 1.

Which of the following plane parametric curves is a parametrization of an ellipse centred at (4, -2)?

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Exam 9: Conics, Parametric Curves, and Polar Curves

Find the arc length of the curve x = , y = dx, 0 ≤ t ≤ ln(2).

Find all the points of intersection of the curves r = sin θ\thetaθ and = cos 2 θ\thetaθ .

Find the area of the region bounded by the hypocycloid x = a θ\thetaθ , y = a θ\thetaθ .

Find the area bounded by the polar graph r = 4 cos( θ\thetaθ ).

Find the area bounded by the larger loop of the curve r = 1 + 2 sin( θ\thetaθ ).

Find the equation of the parabola passing through the point (2, 5), having vertex at the origin and axis of symmetry along the y-axis.

Find the area of the surface generated by rotating the astroid x = a t, y = a t about .

If the equation f( θ\thetaθ ) = g( θ\thetaθ ) has no solutions, then the polar curves and do not intersect.

Find the area of the surface generated by rotating x = t - sin t, y = 1 - cos t where t [0, 2 π\piπ ] about the x-axis.

Find the area of the surface generated by rotating the lemniscate r2 = a2 cos(2 θ\thetaθ ) about the line θ\thetaθ = 0.

The maximum distance of the Earth from the sun is 9.3 × kilometres. The minimum distance is kilometres. The sun is at one focus of the elliptical orbit. Find the distance from the sun to the other focus.

Find the Cartesian equation of the straight line tangent to the plane curve given parametrically by the equations x(t) = + 2t + 2, y(t) = 1 - 3 - 2 at the point on the curve where t = -1.

Find the centre, eccentricity, and foci of the ellipse + = 1.

Which of the following plane parametric curves is a parametrization of an ellipse centred at (4, -2)?

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Find all the points of intersection of the curves r = $Find all the points of intersection of the curves r = sin \theta and = cos 2 \theta .$ sin $\theta$ and $Find all the points of intersection of the curves r = sin \theta and = cos 2 \theta .$ = cos 2 $\theta$ .

Find the area of the region bounded by the hypocycloid x = a $Find the area of the region bounded by the hypocycloid x = a \theta , y = a \theta .$ $\theta$ , y = a $Find the area of the region bounded by the hypocycloid x = a \theta , y = a \theta .$ $\theta$ .

Find the area bounded by the polar graph r = 4 cos( $\theta$ ).

Find the area bounded by the larger loop of the curve r = 1 + 2 sin( $\theta$ ).

Find the area of the surface generated by rotating x = t - sin t, y = 1 - cos t where t $Find the area of the surface generated by rotating x = t - sin t, y = 1 - cos t where t [0, 2 \pi ] about the x-axis.$ [0, 2 $\pi$ ] about the x-axis.

Find the area of the surface generated by rotating the lemniscate r² = a² cos(2 $\theta$ ) about the line $\theta$ = 0.