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Unformatted text preview: MATH023 Review Exercises 1. Find the lengths of the following curves: a. g = 8G¡¢£ + 8£ ¢¤¥£ , ¦ = 8¢¤¥£ − 8£ G¡¢£ from £ = 0 to £ = § ¨ b. g = © ª « + ¬ © ® from ¦ = 1 to ¦ = 2 . Hint: 1 + (dx/dy) 2 is a perfect square. c. 3 , ) ln(cos π ≤ ≤ = x x y d. 1 , 2 cosh 3 2 1 ≤ ≤ + = x x y e. ¯ = ¬ √¨ ° ± , 0 ≤ £ ≤ ² 2. Setup an integral for the length of the following curves and use your calculator to find the curve’s length numerically. a. 3 , tan ≤ ≤ π = x x y b. 2 / 1 2 / 1 , 1 2 ≤ ≤ = y y x c. ) 3 , 7 ( to ) 1 , 1 ( from 1 2 2 2 + = + x y y d. π ≤ ≤ = x x x x y , cos sin 3. Setup an integral for the circumference of the ellipse 3g ¨ + ¦ ¨ = 3 . 4. Find the lateral surface area of the cone generated by revolving the line segment ¦ = ³ ¨ , 0 ≤ g ≤ 4 about the (a) xaxis and (b) yaxis. 5. Find the area of the surface generated by revolving ¯ = 4¢¤¥£ about the (a) polar axis and (b) 90 o line 6. Setup...
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This note was uploaded on 12/08/2011 for the course ECON 101 taught by Professor Smith during the Spring '11 term at Adrian College.
 Spring '11
 SMITH

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