AP Calculus BC Unit 9 – Parametric Equations, Polar Coordinates, and VectorValued Functions
AP Calculus BC Unit 9 – Parametric Equations, Polar Coordinates, and VectorValued Functions
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Question 1 of 19
1. Question
A curve in the plane is defined parametrically by the equations x = 2sin(1+3t) and y= 2t^{3} . Find dy/dx
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Question 2 of 19
2. Question
A curve in the plane is defined parametrically by the equations and . Find the value of at .
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Question 3 of 19
3. Question
A curve is defined by the parametric equations x=3 e^{2t} and y=e ^{3t} −1 . What is in terms of t ?
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Question 4 of 19
4. Question
A curve is defined by the parametric equations x=8 √ t+1 and y=−6 √ t+t . What is in terms of t ?
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Question 5 of 19
5. Question
Consider the parametric curve: ,
Which integral gives the arc length of the curve over the interval from to ?
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Question 6 of 19
6. Question
Consider the parametric curve: x= 5 t ^{2} , y=2 e ^{t} Which integral gives the arc length of the curve over the interval from t =−1 to t =3 ?
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Question 7 of 19
7. Question
Let f be a vectorvalued function defined by Find f'(t) ;
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Question 8 of 19
8. Question
Let g be a vectorvalued function defined by Find g'(t)….
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Question 9 of 19
9. Question
Let h be a vectorvalued function defined by Find h’s second derivative h′′(t).
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Question 10 of 19
10. Question
A particle moves in the xyplane so that at any time t ≥ 0 its coordinates are x= t^{3 }– 2t and y= 3t+1 What is the particle’s velocity vector at t=3 ?
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Question 11 of 19
11. Question
Let r be the polar function r ( θ )=5 θ−1. What is the rate of change of the ycoordinate with respect to θ at the point where θ=π ?
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Question 12 of 19
12. Question
Let r be the polar function Here is its graph for 0 ≤θ ≤ 2 π : What is the rate of change of the xcoordinate with respect to θ at the point P?
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Question 13 of 19
13. Question
Consider the polar curve r=4 sin ( 5 θ) . What is the equation of the tangent line to the curve r at
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Question 14 of 19
14. Question
Let R be the region enclosed by the polar curve Which integral represents the area of R?
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Question 15 of 19
15. Question
Let R be the region enclosed by the polar curve Which integral represents the area of R?
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Question 16 of 19
16. Question
Let R be the region in the second quadrant enclosed by the polar curve r ( θ )=θ+ sin ( θ) and the coordinate axes, as shown in the graph. Which integral represents the area of R?
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Question 17 of 19
17. Question
Let R be the region that is inside the polar curve r = 3 and outside the polar curve r=2+ sin ( θ ) , as shown in the graph. Which integral represents the area of R?
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Question 18 of 19
18. Question
Let R be the region in the second quadrant that is inside the polar curve r= 2 and outside the polar curve r=2+ sin ( 2 θ) , as shown in the graph. Which integral represents the area of R?
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Question 19 of 19
19. Question
Let R be the region inside the polar curve r=cos (θ) and inside the polar curve r=1+ sin ( θ) , as shown in the graph. Which integral represents the area of R?
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