Calculus Problems

Transcribed Text

1. A. Plot the following curves, indicating positive orientation. b. Eliminate the parameter to obtain an equation in x and y. c. Find dy/dx at the specified point in I and ii i. x = t2 + 4, y = 6 – t (5,5) ii. x = 10 sin2t, y = 16 cos2t 0  t  2 (5 3,8) iii. x = sint – 3, y = cos t +6, 0  t  2 2. Graph the following: a. R = 4 b. r = θ c. θ = π/4 d. r = 1 + cos θ e. r = 2cos θ 3. Identify the following curves: a. 4 2 2 x  y  b. 4 16 2 2 x  y  c. 4 0 2 y  x  d. 4 16 4 2 2 x  y  e. 2 3 2 x  y  f. 6 6 48 2 2 x  y  4. Find the slope of the tangent line to the following curves at the points indicated: a. r = 2cos2 θ (2, 0) (-2, π/2) b. R 2 = 2 cos 2 θ (0, π/4) ( 2 , π ) 5. Change the following polar equations to Cartesian equations: a. (-2, π/2) b. ( 2 , π ) 6. Change the following Cartesian equations to polar equations. a. (4,-3) b. (-1, -1) c. (-1, 3 )

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