Adjunct 3.pdf - Math 98 Adjunct for Math 53 Faculty Professor Zworki Adjunct Instructor Mike Wong [email protected] Location MWF 9-10 182 Dwinelle MWF

Adjunct 3.pdf - Math 98 Adjunct for Math 53 Faculty...

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Math 98: Adjunct for Math 53 Faculty: Professor Zworki Adjunct Instructor: Mike Wong, [email protected] Location: MWF 9-10, 182 Dwinelle MWF 12-1, B5 Hearst Field Annex Worksheet 2: Parametric Equations and Polar Coordinates (10.2-10.4) 1) A curve is defined by the parametric equations !(#) = 1 − # ( , )(#) = # * − # a) Find the area of the loop. b) Find the length of the loop. c) Find the concavity at the origin (you should have two answers). 2) Convert each equation into polar coordinates. a) ! ( + ) ( = 1 b) (! − 3) ( + ) ( = 9 c) ! ( + () − 3) ( = 9 d) ) = ! e) ) = √3 ! f) ) = 1 g) ! = 1 3) Sketch each polar curve a) / = 2 b) 1 = 2 3 c) / = 1 ( d) / = cos 1 e) / = sin 1 f) / = 2 cos 1 g) / = 2 cos 91 − 2 : ; h) / = 1 + cos 1 i) / = 2 + cos 1 j) / = 1 + 2 cos 1 k) / = cos 21 l) / = sin 21 m) / = sin 31 n) / = sin 921 + 2 ( ; 4) Consider the polar curve / = 1 + 2 cos 1 . a) Sketch the curve b) Find the area of the inner loop. c) Find the area between the outer loop and the inner loop. 5) Set up the integral for the length of the inner loop of the curve / = 1 + 2 cos 1 . I too t malt by 2 t tint S c c can do full area b c there are 2 neg signs that cancel bottom half neg t x'Its neg O o a 2ft t t 2 t at L

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