around 20 pre calc problems

1. Find the center, vertices, and foci of the ellipse with equation x squared divided by four hundred plus y squared divided by two hundred and fifty six = 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: Ordered pair zero comma negative square root seven and ordered pair zero comma square root seven
Center: (0, 0); Vertices: (0, -9), (0, 9); Foci: Ordered pair zero comma negative square root seventy seven and ordered pair zero comma square root seventy seven
Center: (0, 0); Vertices: (-9, 0), (9, 0); Foci: Ordered pair negative square root seventy seven comma zero and ordered pair square root seventy seven comma zero
Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: Ordered pair negative square root seven comma zero and ordered pair square root seven comma zero
3. Graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1. (2 points)
A vertical ellipse is shown on the coordinate plane centered at, five, two, with vertices at, five, seven, and five, negative three and minor axis endpoints at three, two, and seven, two.
A horizontal ellipse is shown on the coordinate plane centered at five, two, with vertices at zero, two, and ten, two and minor axis endpoints at five, four and five, zero.
A vertical ellipse is shown on the coordinate plane centered at the origin with vertices at zero, five and zero, negative five and minor axis endpoints at, negative two, zero and two, zero.
A horizontal ellipse is shown on the coordinate plane centered at the origin with vertices at, negative five, zero and, five, zero and minor axis endpoints at, zero, two and zero, negative two.
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)
x squared divided by sixty four plus y squared divided by eighty one = 1
x squared divided by nine plus y squared divided by eight = 1
x squared divided by eighty one plus y squared divided by sixty four = 1
x squared divided by eight plus y squared divided by nine = 1
5. An elliptical riding path is to be built on a rectangular piece of property, as shown below.(SHORT ANSWER)

A vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width.

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 2θ, 0 ≤ θ ≤ 2π (2 points)

a circle tangent to the x axis, symmetric about the y axis, and lying in quadrants one and two
[-4, 4] by [-4, 4]
a graph of three loops originating at the origin where one loop lies on and is symmetric about the x axis and the other two loops lie in quadrants two and three
[-4, 4] by [-4, 4]
a graph of four loops originating at the origin lying on and symmetric about the x and y axis
[-4, 4] by [-4, 4]
a graph of four loops originating at the origin where each loop is entirely contained within each quadrant
[-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.

a circle symmetric to the x axis where the majority of the circle lies in quadrants two and three

[-5, 5] by [-5, 5] (2 points)

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

r = -3 – 2 cos θ (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 3θ (3 points)

1. Use the given graph to determine the limit, if it exists. (4 points)

A coordinate graph is shown with a horizontal line crossing the y axis at three that ends at the open point 2, 3, a closed point at 2, 1, and another horizontal line starting at the open point 2, -3.

Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..

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)

A coordinate graph is shown with a downward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and another horizontal line starting at the open point 3, -3.

Find limit as x approaches three from the left of f of x. .

-1
7
-3
Does not exist
3. Use the given graph to determine the limit, if it exists. (4 points) (SHORT ANSWER)

A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.

Find limit as x approaches three from the right of f of x. .

1. Find the indicated limit, if it exists. (2 points)

limit of f of x as x approaches 2 where f of x equals x plus 3 when x is less than 2 and f of x equals 3 minus x when x is greater than or equal to 2

The limit does not exist.
1
2
5
2. Find the indicated limit, if it exists. (2 points)

limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1

6
0
5
The limit does not exist.
3. Find the indicated limit, if it exists. (2 points)

limit of f of x as x approaches 0 where f of x equals 5 x minus 9 when x is less than 0 and the absolute value of the quantity 2 minus x when x is greater than or equal to 0

-9
-7
2
The limit does not exist.
4. Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 4 as x approaches 4 from the left . (2 points)
∞ ; x = -4
-∞ ; x = -4
-∞ ; 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)
 
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