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Quiz 9 Practice Questions - Calculus for Business and the Life Science | MAT 308, Quizzes of Analytical Geometry and Calculus

Material Type: Quiz; Professor: Zhang; Class: Calculus and Analytic Geometry II; Subject: MAT Mathematics; University: Murray State University; Term: Unknown 1989;

Typology: Quizzes

Pre 2010

Uploaded on 08/16/2009

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Quiz/Worksheet #9 MAT 308 - 1
Name............................................ Name............................................
Name............................................
Please staple this cover sheet to your answers. Worksheets not stapled will NOT be
accepted!
Please show your work clearly and neatly. NO work NO credit!
Your group size may have AT MOST 3 people with your name first.
1. Graph the curves and find the area it encloses:
(a) r= sin(3θ) (b) #5 on pp. 683 of the text
(c) r2= 4 cos(2θ) (d) #8 on pp. 683 of the text
2. Find the area of the region that lies in the first curve and outside the second curve:
(a) r= 3 cos(θ) and r= 1 + cos θ
(b) The area inside the larger loop and outside the smaller loop of the lima¸con r=1
2+cos θ
3. Find the exact length of the polar curves:
(a) r= 3 sin θfor 0 θπ/3
(b) r=θ2for 0 θ2π
4. Find the slope of the tangent line to the given polar curve at the point specified by the
value of θ:
(a) r= 1 at θ=π(b) r= 3 cos θat θ=π/3
(c) r= sin θ+ cos θat θ=π/2 (d) r=eθat θ=π/4

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Download Quiz 9 Practice Questions - Calculus for Business and the Life Science | MAT 308 and more Quizzes Analytical Geometry and Calculus in PDF only on Docsity!

Quiz/Worksheet #9 MAT 308 - 1

Name............................................ Name............................................

Name............................................

  • Please staple this cover sheet to your answers. Worksheets not stapled will NOT be accepted!
  • Please show your work clearly and neatly. NO work – NO credit!
  • Your group size may have AT MOST 3 people with your name first.
  1. Graph the curves and find the area it encloses: (a) r = sin(3θ) (b) #5 on pp. 683 of the text

(c) r^2 = 4 cos(2θ) (d) #8 on pp. 683 of the text

  1. Find the area of the region that lies in the first curve and outside the second curve:

(a) r = 3 cos(θ) and r = 1 + cos θ

(b) The area inside the larger loop and outside the smaller loop of the lima¸con r =

+cos θ

  1. Find the exact length of the polar curves:

(a) r = 3 sin θ for 0 ≤ θ ≤ π/ 3

(b) r = θ^2 for 0 ≤ θ ≤ 2 π

  1. Find the slope of the tangent line to the given polar curve at the point specified by the value of θ: (a) r = 1/θ at θ = π (b) r = 3 cos θ at θ = π/ 3

(c) r = sin θ + cos θ at θ = π/ 2 (d) r = eθ^ at θ = π/ 4