1. Jeopardy Final Jeopardy Limits Rate of Δ Graphs Position Potpourri
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Final Jeopardy

2. Limits - $100 The limit as x approaches 0 of f(x)=3x/x by limit def.
What is 3?
This question teaches the basics of defining of a limit as x approaches 0 due to the multiplicative property of association because 3x/x is equal to 3(x/x) which equals 3.

3. Limits - $200
The limit as x approaches 3 of the function f(x) = 5/(x-3)
What is DNE?

4. Limits - $300 The limit as x approaches 9 of (1/x – 1/9)/(x-9)
What is -1/81?

5. Limits - $400
The limit as h approaches 0 of the function ((1+h)1/2 – 1)/h.
What is 1/2?

6. Limits - $500
The limit as x approaches 2 of the function f(x) = (abs(x-2))/(x-2)
What is DNE?

7. Rate of Δ - $100
Given point A and point B of a continuous function, with point A at (0,3) and point B at (7,14), this quantity represents the average rate of change over the interval from point A to point B
What is 11/7?

8. Rate of Δ - $200
Using linear approximation, this quantity represents the value when x=3.2 of the function f(x)=x5
What is 362?

9. Rate of Δ - $300
Given point A and point B of a continuous function, with point A at (4,-3) and point B at (6,0), this integer, representing an x-value, must exist over the function
What is 5?

10. Rate of Δ - $400
An open box exists having a square base and surface area of 108 square inches. This quantity represents the dimensions of such box with maximum volume.
What is 6X6X3?

11. Rate of Δ - $500 What is 90 square feet per day?
The desks in Mr. Farrar’s class are arranged in a rectangular figure with all desks equal height. From the front to back of the class, the length of the space occupied by the desks is 30 ft. Every day, the space occupied by the desks widens by 3 ft. When the width of the area is 48 ft, this quantity represents how fast the area is changing.
What is 90 square feet per day?

12. Graphs - $100
The second derivative is positive between these intervals
What is (a,b) and (c,d)?

13. Graphs - $200
Sketch a graph where f’’(x) is always positive and f’(x) goes from positive to x=-3 with zeroes at x= -1 and -5

14. Graphs - $300 f(x)=|x2-9| is not differentiable at these points.
What is (3,0) (-3,0)?

15. Graphs - $400
These represent the rel. extrema of the function f(x)=x4-2x2 on the interval [-2,2]
What is a Rel. min at (1,-1) (-1,-1) and rel. max at (0,0)?

16. Graphs - $500
What is an abs. max at (π/6 , (3/2)31/2) and min at (π/2 , 0)?

17. Position - $100 What is 282 meters?
The velocity of a particle moving along the x axis at time t is represented by the function f(t)=5t2/3+6t. This quantity represents the total distance travelled by the particle from t=1 to t=8 seconds.
What is 282 meters?

18. Position - $200
The displacement of an object moving in a straight line is given by s(t)=1+2t+t2/4. This quantity represents the instantaneous velocity at t=1 second.
What is 2.5 m/s?

19. Position - $300
A bottle rocket shot upward from a 10 ft stand has velocity as represented in the function v(t)=50-1.6t. This quantity represents the time at which the rocket hits maximum height.
What is seconds?

20. Position - $400
A particle is positioned along the x-axis as represented by the function f(x)=x3+8x2+9. This quantity represents the particle’s acceleration when velocity is 12 m/s.
What is 20 m/s/s?

21. Position - $500
Given the position function of a particle being s(t)=2t3-9t2, this duration represents the period at which the particle is speeding up.
What is (0,3/2) & (3,∞)?

22. Potpourri - $100 The first derivative of f(x)=sin-1(k48cos(k))
What is 0?

23. Potpourri - $200
The equation of the horizontal asymptote of the function f(x)=(73x2)/√(14x5)
What is x=0?

24. Potpourri - $300
The function f(x) such that the point (0,5) exists and 18x+4 is the first derivative of the function
What is f(x)=9x2+4x+5?

25. Potpourri - $400 The fourth derivative of the function f(x)=42
What is 0?

26. Potpourri - $500 33
What is 27?

27. Final Jeopardy
A particle moves along the x-axis, starting at x=0 and stopping at x=5, with an initial velocity of 18m/s according to this position function.
s(x)=(-5/36)x2+18x