# around 20 pre calc problems

1. Find the center, vertices, and foci of the ellipse with equation = 1. (2 points)
 Center: (0, 0); Vertices: (-20, 0), (20, 0); Foci: (-12, 0), (12, 0) Center: (0, 0); Vertices: (-20, 0), (20, 0); Foci: (-16, 0), (16, 0) Center: (0, 0); Vertices: (0, -20), (0, 20); Foci: (0, -16), (0, 16) Center: (0, 0); Vertices: (0, -20), (0, 20); Foci: (0, -12), (0, 12)
2. Find the center, vertices, and foci of the ellipse with equation 2x2 + 9y2 = 18. (2 points)
 Center: (0, 0); Vertices: (0, -3), (0, 3); Foci: Center: (0, 0); Vertices: (0, -9), (0, 9); Foci: Center: (0, 0); Vertices: (-9, 0), (9, 0); Foci: Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: 3. Graph the ellipse with equation = 1. (2 points)    4. Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 16. (2 points) = 1 = 1 = 1 = 1
 5 An elliptical riding path is to be built on a rectangular piece of property, as shown below.(SHORT ANSWER) The rectangular piece of property measures 8 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides. (2 points)
1. Draw a graph of the rose curve.

r = 4 cos 2Î¸, 0 â‰¤ Î¸ â‰¤ 2Ï€ (2 points) [-4, 4] by [-4, 4] [-4, 4] by [-4, 4] [-4, 4] by [-4, 4] [-4, 4] by [-4, 4]
2. The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. [-5, 5] by [-5, 5] (2 points)

 r = 2 – 2 cos Î¸ r = 3 – 2 cos Î¸ r = 3 – cos Î¸ r = 3 – sin Î¸
3. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = -3 – 2 cos Î¸ (3 points)

 No symmetry y-axis only Origin only x-axis only
 4 Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. (SHORT ANSWER) r = 5 cos 3Î¸ (3 points)
1. Use the given graph to determine the limit, if it exists. (4 points) Find and .

 1; 1 3; -3 Does not exist; does not exist -3; 3
2. Use the given graph to determine the limit, if it exists. (2 points) Find .

 -1 7 -3 Does not exist
 3 Use the given graph to determine the limit, if it exists. (4 points) (SHORT ANSWER) Find .
1. Find the indicated limit, if it exists. (2 points) The limit does not exist. 1 2 5
2. Find the indicated limit, if it exists. (2 points) 6 0 5 The limit does not exist.
3. Find the indicated limit, if it exists. (2 points) -9 -7 2 The limit does not exist.
4. Use graphs and tables to find the limit and identify any vertical asymptotes of . (2 points)
 âˆž ; x = -4 -âˆž ; x = -4 -âˆž ; x = 4 1 ; no vertical asymptotes
 5 Give an example of a function with both a removable and a non-removable discontinuity. (2 points) (SHORT ANSWER) 