# Section 9.3 Parametric Equations and Calculus

Education

22

All Questions

22

Multiple Choice

0

True False

0

Essay

0

Short Answer

0

Not Answered

Q 1

Find .
A)
B)
C)
D)
E)

Free

Multiple Choice

C

Q 2

Find .
A)
B)
C)
D)
E)

Free

Multiple Choice

B

Q 3

Find .
A)
B)
C)
D)
E)

Free

Multiple Choice

E

Q 4

Find the second derivative of the parametric equations , .Round your answer to two decimal places,if necessary.
A)0
B)0.38
C)
D)2.67
E)

Multiple Choice

Q 5

Find and if possible,and find the slope and concavity (if possible)at the point corresponding to .
A) , at
: slope
and concave up
B) , ;at
: slope
and concave down
C) , ;at
: slope
and concave up
D) , ;at
: slope
and concave down
E) , at
: slope
and concave up

Multiple Choice

Q 6

Find and if possible,and find the slope and concavity (if possible)at the point corresponding to .
A) ,
;at
: slope
and concave down
B) , ;at
: slope
and concave down
C) ,
;at
: slope
and concave up
D) , ;at
: slope
and concave up
E) , ;at
: slope of
and concave down

Multiple Choice

Q 7

Find the second derivative of the parametric equations , .
A)
B)
C)
D)
E)

Multiple Choice

Q 8

Find an equation of the tangent line at a point on the curve , .
A)
B)
C)
D)
E)

Multiple Choice

Q 9

Find all points (if any)of horizontal and vertical tangency to the curve , .
A)horizontal tangents: ,vertical tangent: none
B)horizontal tangent: none,vertical tangents:
C)horizontal tangents: ,vertical tangent: none
D)horizontal tangent: none,vertical tangents:
E)horizontal tangent: none,vertical tangent: none

Multiple Choice

Q 10

Find all points (if any)of horizontal and vertical tangency to the curve , .
A)horizontal tangents: ,vertical tangents:
B)horizontal tangents: ,vertical tangents:
C)horizontal tangent: ,vertical tangent:
D)horizontal tangents: ,vertical tangents:
E)horizontal tangent: ,vertical tangent:

Multiple Choice

Q 11

Determine the t intervals on which the curve , is concave downward or concave upward.
A)concave downward: ;concave upward:
B)concave downward: ;concave upward:
C)concave downward: ;concave upward:
D)concave downward: ;concave upward:
E)concave downward: ;concave upward:

Multiple Choice

Q 12

Determine the t intervals on which the curve , is concave downward or concave upward.
A)concave downward: ;concave upward:
B)concave downward: ;concave upward:
C)concave downward:
D)concave upward:
E)concave downward:

Multiple Choice

Q 13

Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)

Multiple Choice

Q 14

Find the arc length of the curve , on the interval .Round your answer to three decimal places.
A)384.650
B)256.433
C)259.131
D)89.195
E)133.793

Multiple Choice

Q 15

Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)

Multiple Choice

Q 16

Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)

Multiple Choice

Q 17

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet.Use a graphing utility to approximate the range of the projectile.Round your answer to two decimal places.
A)327.75 ft
B)546.25 ft
C)137.33 ft
D)409.68 ft
E)204.84 ft

Multiple Choice

Q 18

The path of a projectile is modeled by the parametric equations and where x and y are measured in feet.Use the integration capabilities of a graphing utility to approximate the arc length of the path.Round your answer to one decimal place.
A)434.1 ft
B)667.9 ft
C)375.6 ft
D)302.6 ft
E)521.8 ft

Multiple Choice

Q 19

Find the area of the surface generated by revolving the curve , about the x-axis on the interval .
A)
B)
C)
D)
E)

Multiple Choice

Q 20

Find the area of the surface generated by revolving the curve about the given axis.
(i)x-axis; (ii)y-axis
A)
B)
C)
D)
E)

Multiple Choice

Q 21

Find the area of the surface generated by revolving the curve , about the y-axis on the interval .Round your answer to two decimal places.
A)1,427.12
B)1,178.96
C)1,049.37
D)589.48
E)1,898.04

Multiple Choice

Q 22

Find the area of the surface generated by revolving the curve about the given axis. (i)x-axis; (ii)y-axis
A)
B)
C)
D)
E)

Multiple Choice