1. Calculator Review #2 What is the average value of the function
on the interval [1, 3]?
0.146
0.914
0.964
0.987
1.928
Use Average Value for Integrals
Ans: C

2. Calculator Review #2
Right triangle ABC has its right angle at A. Leg AB is decreasing at a constant rate of 3cm per minute. Leg AC is increasing at a constant rate of 4 cm per minute. How is the hypotenuse BC changing at the moment when AB = 12 and AC =5?
It is decreasing at the rate of 16 cm per minute
It is decreasing at the rate of 16/13 cm per minute
It is not changing
It is increasing at the rate of 33/13 cm per minute
It is increasing at the rate of 16 cm per minute.
This is a derivative/related rate problem C a b
A c B

3. Calculator Review #2 The fundamental theorem of calculus Ans: D 3.
2.163
2.660
2.780
5.163
5.660
The fundamental theorem of calculus
Ans: D

4. Calculator Review #2 Max/Min problem
This function is the derivative of f(x)
Graph f’(x) then look for zeros, that is, where the function crosses x axis.
1/2
-1/
Ans: D
4. The derivative of a function f is given by f’(x) = sin (cos x) – 0.1x. How many critical points does f have on the open interval (0, 8)?
None
One
Two
Three
Four

5. Calculator Review #2 Area - Integrals Ans: A
What is the area of the region bounded by the graphs of
1.523
2.358
2.493
4.783
7.409
Area - Integrals
Ans: A

6. Calculator Review #2
6. What is the x-value of the point at which the tangent line to the graph of
-0.732
-0.589
-0.162
0.236
0.361
Tangent Lines - Deriv
Ans: A

7. Calculator Review #2 Volume – Integration outer inner
The region enclosed by the graphs of
and the vertical lines x = 0 and x = 2 is rotated about the y = -3. Which of the following gives the volume of the generated solid?
Volume – Integration
outer
inner
y=-3

8. Calculator Review #2 Graph And y = 2
Which of the following is an equation of the tangent line to the graph of the function
at the point where f’(x) = 2?
A. y = 2x – 0.630
B. y = 2x
C. y = 2x
D. y = 2x
E. y = 2x
Graph
And y = 2
Look for the points of intersection
When x = .315, find f(.315)

9. Calculator Review #2 Differential Equation Growth and Decay
The population of bacteria given by y(t) grows according to the equation
where k is a constant and t is measured in minutes. If y(10) = 10 and
y(30) = 25, what is the value of k? A B C D E
Differential Equation
Growth and Decay

10. Calculator Review #2
The function is continuous on the closed interval [0, 3] and has values that are given in the table below. Using the subintervals
[0, 1] [1, 2] [2, 3], what is the approximation to x 1 2 3
f(x) 5 4

11. Calculator Review #2
Because of rainfall from 9am on a given day, water enters an open reservoir at the rate of
where R(t) is measured in gallons per hour and t is measured in hours after 9am (so 0 <= t <= 12). To prevent overflow, water is pumped out of the reservoir at the constant rate of k gallons per hour. The reservoir holds 500,000 gallons of water both at 9am and 9pm.
A. What is k? Round your answer to the nearest whole number.

12. Calculator Review #2
Because of rainfall from 9am on a given day, water enters an open reservoir at the rate of
where R(t) is measured in gallons per hour and t is measured in hours after 9am (so 0 <= t <= 12). To prevent overflow, water is pumped out of the reservoir at the constant rate of k gallons per hour. The reservoir holds 500,000 gallons of water both at 9am and 9pm.
B. To the nearest gallon, how much water is the reservoir at 7pm (t = 10)?
Want to find the adding water and leaving water. The combined rate is W’(t) = R(t) – k Know: W(0)= k =

13. Calculator Review #2
Because of rainfall from 9am on a given day, water enters an open reservoir at the rate of
where R(t) is measured in gallons per hour and t is measured in hours after 9am (so 0 <= t <= 12). To prevent overflow, water is pumped out of the reservoir at the constant rate of k gallons per hour. The reservoir holds 500,000 gallons of water both at 9am and 9pm.
C. At what time t, for 0<= t <= 12, does the reservoir hold the greatest amount of water?
W’(t) = R(t) – k Graph this function and find the zeros. t = and t = These are between 0 and 12 Determine what happens at these points. At x = the function increases then decreases, so this is a max

14. Calculator Review #2
The table below gives the velocity v(t) at selected times t of a car traveling along a straight road.
A. Use the values of the table to approximate the acceleration of the car at time t = 6. Show the work that leads to your answer and indicate units of measure.
Find the average acceleration by using T 2 5 7 8 10
V(t) 50 55 60 70 65 75

15. Calculator Review #2
The table below gives the velocity v(t) at selected times t of a car traveling along a straight road.
Use a right Riemann sum with the subintervals given in the table to approximate
Indicate units of measure. What physical quantity does this integral represent? T 2 5 7 8 10
V(t) 50 55 60 70 65 75

16. Calculator Review #2
The table below gives the velocity v(t) at selected times t of a car traveling along a straight road.
C. The function v(t) is twice differentiable on the interval [0,10]. Show that there must be a moment of time when the acceleration of he car is equal to zero.
Choose a small interval on [5,8] V(7) = 70 V(8) = 65 V(5) = 60 V(7) is greater than this small interval of [5,8] Intermediate value theorem: find some c within [5,7] with v ( c ) = 65 The mean value theorem guarantees a point somewhere on [c,8] where v’ is zero. T 2 5 7 8 10
V(t) 50 55 60 70 65 75