1. Find the standard form of the equation of the parabola with a focus at (0, 4) and a directrix at y = -4. a) y = 1 divided by 16x2

b) y2 = 16x

c) y2 = 4x

d) y = 1 divided by 4x2

2. Find the first six terms of the sequence.

a1 = -7, an = 2 • an-1

a) -7, -14, -12, -10, -8, -6

b) 0, 2, -14, -12, -10, -8

c) -7, -14, -28, -56, -112, -224

d) -14, -28, -56, -112, -224, -448

3. Write the sum using summation notation, assuming the suggested pattern continues.

2 - 8 + 32 - 128 + ...

a) summation of 2 times 4 to the power of the quantity n plus 1 from n equals 0 to infinity

b) summation of 2 times negative 4 to the power of the quantity n minus 1 from n equals 0 to infinity

c) summation of 2 times negative 4 to the power of n from n equals 0 to infinity

d) summation of 2 times 4 to the power of n from n equals 0 to infinity

4. Find the limit of the function by using direct substitution.

limit as x approaches zero of quantity x squared plus one.

a) 0

b) -1

c) 1

d) Does not exist

5. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and asymptotes at y = ±3 divided by 7.x.

a) y squared over 36 minus x squared over 196 = 1

b) y squared over 196 minus x squared over 36 = 1

c) y squared over 36 minus x squared over 49 = 1

d) y squared over 49 minus x squared over 9 = 1

6. Find the center, vertices, and foci of the ellipse with equation 3x2 + 8y2 = 24.

a) Center: (0, 0); Vertices: (0, -8), (0, 8); Foci: Ordered pair 0 comma negative square root 55 and ordered pair 0 comma square root 55

b) Center: (0, 0); Vertices: the point negative two square root of two comma zero comma the point positive two square root of two comma zero; Foci: Ordered pair negative square root 5 comma 0 and ordered pair square root 5 comma 0

c) Center: (0, 0); Vertices: (-8, 0), (8, 0); Foci: Ordered pair negative square root 55 comma 0 and ordered pair square root 55 comma 0

d) Center: (0, 0); Vertices: ordered pair zero comma negative 2 square root 2 and ordered pair zero comma 2 square root 2; Foci: ordered pair zero comma negative square root 5 and ordered pair zero comma square root 5

7. Find the center, vertices, and foci of the ellipse with equation x squared divided by 9 plus y squared divided by 25 = 1.

a) Center: (0, 0); Vertices: (-5, 0), (5, 0); Foci: (0, -3), (0, 3)

b) Center: (0, 0); Vertices: (0, -5), (0, 5); Foci: (0, -4), (0, 4)

c) Center: (0, 0); Vertices: (-5, 0), (5, 0); Foci: (-4, 0), (4, 0)

d) Center: (0, 0); Vertices: (0, -5), (0, 5); Foci: (-3, 0), (3, 0)

EXPLAIN AND SHOW WORK FOR THE FOLLOWING PROBLEMS!!!

8. Use graphs and tables to find the limit and identify any vertical asymptotes of the function.

limit of 1 divided by the quantity x minus 8 as x approaches 8 from the left

9. Find the fifth roots of 243(cos 300° + i sin 300°).

10. The position of an object at time t is given by s(t) = -9 - 5t. Find the instantaneous velocity at t = 4 by finding the derivative.

11. Use the given graph to determine the limit, if it exists.

A coordinate graph is shown with a horizontal line crossing the y axis at five that ends at the open point 2, 5, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 2 and continues to the right.

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..