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9.06

1. find the derivative of f(x) = -4x2 + 11x at x = 10.

a) -19.5
b) -69
c) 30
d) -300

2. find the derivative of f(x) = 8x + 4 at x = 9.

a) 0
b) 4
c) 8
d) 9

3. find the derivative of f(x) = 4 divided by x at x = 2.

a) -4
b) -1
c) 1
d) 4

4. find the derivative of f(x) = negative 9 divided by x at x = -4.

a) 4 divided by 9
b) 16 divided by 9
c) 9 divided by 16
d) 9 divided by 4

5. find the limit of the function by using direct substitution.
limit as x approaches zero of quantity x squared plus five.

a) does not exist
b) -5
c) 0
d) 5

6. find the limit of the function by using direct substitution.
limit as x approaches four of quantity x squared plus three x minus one

a) does not exist
b) -27
c) 0
d) 27

7. find the limit of the function algebraically.
limit as x approaches four of quantity x squared minus sixteen divided by quantity x minus four.

a) does not exist
b) 4
c) 1
d) 8

8. find the limit of the function algebraically.
limit as x approaches zero of quantity x squared minus two x divided by x to the fourth power.

a) does not exist
b) 8
c) 0
d) -8

9. 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 four that ends at the open point 2, 4, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 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.

a) -3; 4
b) 1; 1
c) 4; -3
d) does not exist; does not exist

10. use the given graph to determine the limit, if it exists.
a coordinate graph is shown with a downward sloped line crossing the y axis at the origin that ends at the open point 3, negative 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, negative 4.

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

a) -1
b) 7
c) -4
d) does not exist

11. find the indicated limit, if it exists.
limit of f of x as x approaches negative 1 where f of x equals x plus 1 when x is less than negative 1 and f of x equals 1 minus x when x is greater than or equal to negative 1

a) -1
b) 2
c) the limit does not exist.
d) 0

12. find the indicated limit, if it exists.
limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and negative 10 x plus 7 when x is greater than 0

a) the limit does not exist.
b) 7
c) -10
d) -17

13. use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 3 as x approaches 3 from the left.

a) ∞; x = -3
b) -∞; x = -3
c) -∞; x = 3
d) 1 ; no vertical asymptotes

14. the position of an object at time t is given by s(t) = -1 - 13t. find the instantaneous velocity at t = 8 by finding the derivative.

15. 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 1 squared as x approaches 1