Question 1

The rectangular equation of the conic section $r = \frac { 2 } { 5 + 3 \cos \theta }$ is

Accepted Answer

A)  $25 x ^ { 2 } - 8 x = 2$ 
B)  $16 x ^ { 2 } + 25 y ^ { 2 } + 12 x = 4$ 
C)  $16 x ^ { 2 } + 25 y ^ { 2 } - 12 y = 4$ 
D)  $16 x ^ { 2 } + 25 y ^ { 2 } - 12 x = 4$ 
E)  $16 x ^ { 2 } + 25 y ^ { 2 } + 12 y = 4$ 
A)  $25 x ^ { 2 } - 8 x = 2$ 
B)  $16 x ^ { 2 } + 25 y ^ { 2 } + 12 x = 4$ 
C)  $16 x ^ { 2 } + 25 y ^ { 2 } - 12 y = 4$ 
D)  $16 x ^ { 2 } + 25 y ^ { 2 } - 12 x = 4$ 
E)  $16 x ^ { 2 } + 25 y ^ { 2 } + 12 y = 4$

Question 2

The area of the surface generated by revolving the curve $x ( t ) = \frac { 2 t ^ { \frac { 3 } { 2 } } } { 3 } , y = 2 \sqrt { t }$ with $t \in [ 0 , \sqrt { 3 } ]$ about the y-axis is

Accepted Answer

A)  $\frac { 28 \pi } { 7 }$ 
B)  $\frac { 29 \pi } { 8 }$ 
C)  $\frac { 28 \pi } { 9 }$ 
D)  $\frac { 27 \pi } { 8 }$ 
E)  $\frac { 29 \pi } { 9 }$ 
A)  $\frac { 28 \pi } { 7 }$ 
B)  $\frac { 29 \pi } { 8 }$ 
C)  $\frac { 28 \pi } { 9 }$ 
D)  $\frac { 27 \pi } { 8 }$ 
E)  $\frac { 29 \pi } { 9 }$

Question 3

The parametric equations of the line segment from (-5,0) to (0,5) with t $\in$[0,5] are

Accepted Answer

A)  $x ( t ) = 5 - t , y ( t ) = t$ 
B)  $x ( t ) = t , y ( t ) = 5 - t$ 
C)  $x ( t ) = t , y ( t ) = t - 5$ 
D)  $x ( t ) = t - 5 , y ( t ) = t$ 
E)  $x ( t ) = t - 5 , y ( t ) = 5 - t$ 
A)  $x ( t ) = 5 - t , y ( t ) = t$ 
B)  $x ( t ) = t , y ( t ) = 5 - t$ 
C)  $x ( t ) = t , y ( t ) = t - 5$ 
D)  $x ( t ) = t - 5 , y ( t ) = t$ 
E)  $x ( t ) = t - 5 , y ( t ) = 5 - t$

Question 4

If A is the area of the region bounded by one petal of the five-petal rose $r = \sin 5 \theta,$ then A is

Accepted Answer

A)  $\frac { \pi } { 2 }$ 
B)  $\frac { \pi } { 3 }$ 
C)  $\frac { \pi } { 5 }$ 
D)  $\frac { \pi } { 10 }$ 
E)  $\frac { \pi } { 20 }$ 
A)  $\frac { \pi } { 2 }$ 
B)  $\frac { \pi } { 3 }$ 
C)  $\frac { \pi } { 5 }$ 
D)  $\frac { \pi } { 10 }$ 
E)  $\frac { \pi } { 20 }$

Question 5

If A is the area of the intersection of the regions inside $r = 3 \cos \theta$ and outside $r = 1 + \cos \theta,$ A is

Accepted Answer

A)  $6 \pi - 16$ 
B)  $3 \sqrt { 3 } - \pi$ 
C)  $\frac { \pi + 1 } { 2 }$ 
D)  $\pi$ 
E)  $\frac { 8 - \pi } { 4 }$ 
A)  $6 \pi - 16$ 
B)  $3 \sqrt { 3 } - \pi$ 
C)  $\frac { \pi + 1 } { 2 }$ 
D)  $\pi$ 
E)  $\frac { 8 - \pi } { 4 }$

Question 6

The rectangular equation that corresponds to the polar equation $\cot \theta = 5$ is

Accepted Answer

A)  $y = \frac { x } { 5 }$ 
B)  $y = - \frac { x } { 5 }$ 
C)  $x = \frac { y } { 5 }$ 
D)  $x = - \frac { y } { 5 }$ 
E)  $x ^ { 2 } + y ^ { 2 } = 25$ 
A)  $y = \frac { x } { 5 }$ 
B)  $y = - \frac { x } { 5 }$ 
C)  $x = \frac { y } { 5 }$ 
D)  $x = - \frac { y } { 5 }$ 
E)  $x ^ { 2 } + y ^ { 2 } = 25$

Question 7

Which one of the following sets of parametric equations does not correspond to the rectangular equation $y = 6 x ^ { 3 } ?$

Accepted Answer

A)  $x ( t ) = t , y ( t ) = 6 t ^ { 3 }$ 
B)  $x ( t ) = 2 t , y ( t ) = 48 t ^ { 3 }$ 
C)  $x ( t ) = \sqrt [ 3 ] { t } , y ( t ) = 6 t$ 
D)  $x ( t ) = t ^ { 4 } , y ( t ) = 6 t ^ { 6 }$ 
E)  $x ( t ) = \frac { \sqrt [ 3 ] { t } } { 2 } , y ( t ) = \frac { 3 t } { 4 }$ 
A)  $x ( t ) = t , y ( t ) = 6 t ^ { 3 }$ 
B)  $x ( t ) = 2 t , y ( t ) = 48 t ^ { 3 }$ 
C)  $x ( t ) = \sqrt [ 3 ] { t } , y ( t ) = 6 t$ 
D)  $x ( t ) = t ^ { 4 } , y ( t ) = 6 t ^ { 6 }$ 
E)  $x ( t ) = \frac { \sqrt [ 3 ] { t } } { 2 } , y ( t ) = \frac { 3 t } { 4 }$

Question 8

The rectangular equation that corresponds to the polar equation $r = - 7 \sin \theta$ is

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } = - 7 y$ 
B)  $x ^ { 2 } + y ^ { 2 } = - 7 x$ 
C)  $x ^ { 2 } + y ^ { 2 } = 7 y$ 
D)  $x ^ { 2 } + y ^ { 2 } = 7 x$ 
E)  $x ^ { 2 } + y ^ { 2 } = \frac { y } { 7 }$ 
A)  $x ^ { 2 } + y ^ { 2 } = - 7 y$ 
B)  $x ^ { 2 } + y ^ { 2 } = - 7 x$ 
C)  $x ^ { 2 } + y ^ { 2 } = 7 y$ 
D)  $x ^ { 2 } + y ^ { 2 } = 7 x$ 
E)  $x ^ { 2 } + y ^ { 2 } = \frac { y } { 7 }$

Question 9

The conic section $r = \frac { 4 } { 2 - \cos \theta }$ is

Accepted Answer

A) A straight line 
B) A circle 
C) A parabola 
D) An ellipse 
E) A hyperbola 
A) A straight line 
B) A circle 
C) A parabola 
D) An ellipse 
E) A hyperbola

Question 10

The rectangular equation of the conic section $r = \frac { 2 } { 4 - 3 \cos \theta }$ is

Accepted Answer

A)  $7 x ^ { 2 } + 16 y ^ { 2 } - 12 x = 4$ 
B)  $16 x ^ { 2 } + 7 y ^ { 2 } + 12 y = 9$ 
C)  $16 x ^ { 2 } + 7 y ^ { 2 } - 12 x = 9$ 
D)  $7 x ^ { 2 } + 16 y ^ { 2 } - 12 y = 4$ 
E)  $7 y ^ { 2 } - 2 y = 4$ 
A)  $7 x ^ { 2 } + 16 y ^ { 2 } - 12 x = 4$ 
B)  $16 x ^ { 2 } + 7 y ^ { 2 } + 12 y = 9$ 
C)  $16 x ^ { 2 } + 7 y ^ { 2 } - 12 x = 9$ 
D)  $7 x ^ { 2 } + 16 y ^ { 2 } - 12 y = 4$ 
E)  $7 y ^ { 2 } - 2 y = 4$

Question 11

For a$\neq$ 0, the polar curve $r = a \sin 4 \theta$ is a

Accepted Answer

A) Circle 
B) Four-petal rose 
C) Eight-petal rose 
D) Cardioid 
E) Limaçon 
A) Circle 
B) Four-petal rose 
C) Eight-petal rose 
D) Cardioid 
E) Limaçon

Question 12

For a $\neq$ 0, the polar curve $r = a \cos 3 \theta$ is a

Accepted Answer

A) Circle 
B) Three-petal rose 
C) Five-petal rose 
D) Cardioid 
E) Limaçon 
A) Circle 
B) Three-petal rose 
C) Five-petal rose 
D) Cardioid 
E) Limaçon

The rectangular equation of the conic section $r = \frac { 2 } { 5 + 3 \cos \theta }$ is

The area of the surface generated by revolving the curve $x ( t ) = \frac { 2 t ^ { \frac { 3 } { 2 } } } { 3 } , y = 2 \sqrt { t }$ with $t \in [ 0 , \sqrt { 3 } ]$ about the y-axis is

The parametric equations of the line segment from (-5,0) to (0,5) with t $\in$ [0,5] are

If A is the area of the region bounded by one petal of the five-petal rose $r = \sin 5 \theta,$ then A is

If A is the area of the intersection of the regions inside $r = 3 \cos \theta$ and outside $r = 1 + \cos \theta,$ A is

The rectangular equation that corresponds to the polar equation $\cot \theta = 5$ is

Which one of the following sets of parametric equations does not correspond to the rectangular equation $y = 6 x ^ { 3 } ?$

The rectangular equation that corresponds to the polar equation $r = - 7 \sin \theta$ is

The conic section $r = \frac { 4 } { 2 - \cos \theta }$ is

The rectangular equation of the conic section $r = \frac { 2 } { 4 - 3 \cos \theta }$ is

For a $\neq$ 0, the polar curve $r = a \sin 4 \theta$ is a

For a $\neq$ 0, the polar curve $r = a \cos 3 \theta$ is a

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Exam 10: Parametric Equations; Polar Equations

The rectangular equation of the conic section r=25+3cos⁡θr = \frac { 2 } { 5 + 3 \cos \theta }r=5+3cosθ2​ is

The area of the surface generated by revolving the curve x(t)=2t323,y=2tx ( t ) = \frac { 2 t ^ { \frac { 3 } { 2 } } } { 3 } , y = 2 \sqrt { t }x(t)=32t23​​,y=2t​ with t∈[0,3]t \in [ 0 , \sqrt { 3 } ]t∈[0,3​] about the y-axis is

The parametric equations of the line segment from (-5,0) to (0,5) with t ∈\in∈ [0,5] are

If A is the area of the region bounded by one petal of the five-petal rose r=sin⁡5θ,r = \sin 5 \theta,r=sin5θ, then A is

If A is the area of the intersection of the regions inside r=3cos⁡θr = 3 \cos \thetar=3cosθ and outside r=1+cos⁡θ,r = 1 + \cos \theta,r=1+cosθ, A is

The rectangular equation that corresponds to the polar equation cot⁡θ=5\cot \theta = 5cotθ=5 is

Which one of the following sets of parametric equations does not correspond to the rectangular equation y=6x3?y = 6 x ^ { 3 } ?y=6x3?

The rectangular equation that corresponds to the polar equation r=−7sin⁡θr = - 7 \sin \thetar=−7sinθ is

The conic section r=42−cos⁡θr = \frac { 4 } { 2 - \cos \theta }r=2−cosθ4​ is

The rectangular equation of the conic section r=24−3cos⁡θr = \frac { 2 } { 4 - 3 \cos \theta }r=4−3cosθ2​ is

For a ≠\neq= 0, the polar curve r=asin⁡4θr = a \sin 4 \thetar=asin4θ is a

For a ≠\neq= 0, the polar curve r=acos⁡3θr = a \cos 3 \thetar=acos3θ is a

Preparing for Calculus

Limits and Continuity

The Derivative

More About Derivatives

Applications of the Derivative

The Integral

Applications of the Integral

Techniques of Integration

Infinite Series

Vectors; Lines, Planes, and Quadric Surfaces in Space

Vector Functions

Functions of Several Variables

Directional Derivatives, Gradients, and Extrema

Multiple Integrals

Vector Calculus

Differential Equations

Filters

The rectangular equation of the conic section $r = \frac { 2 } { 5 + 3 \cos \theta }$ is

The area of the surface generated by revolving the curve $x ( t ) = \frac { 2 t ^ { \frac { 3 } { 2 } } } { 3 } , y = 2 \sqrt { t }$ with $t \in [ 0 , \sqrt { 3 } ]$ about the y-axis is

The parametric equations of the line segment from (-5,0) to (0,5) with t $\in$ [0,5] are

If A is the area of the region bounded by one petal of the five-petal rose $r = \sin 5 \theta,$ then A is

If A is the area of the intersection of the regions inside $r = 3 \cos \theta$ and outside $r = 1 + \cos \theta,$ A is

The rectangular equation that corresponds to the polar equation $\cot \theta = 5$ is

Which one of the following sets of parametric equations does not correspond to the rectangular equation $y = 6 x ^ { 3 } ?$

The rectangular equation that corresponds to the polar equation $r = - 7 \sin \theta$ is

The conic section $r = \frac { 4 } { 2 - \cos \theta }$ is

The rectangular equation of the conic section $r = \frac { 2 } { 4 - 3 \cos \theta }$ is

For a $\neq$ 0, the polar curve $r = a \sin 4 \theta$ is a

For a $\neq$ 0, the polar curve $r = a \cos 3 \theta$ is a