Calc Multiple Choice
4 – 3cos(x)
2 – 3cos(x)
2 – 3cos(x)
4 – 3cos(x)
1.

Find the particular solution to y ′ = 3sin(x) given the general solution is y = C − 3cos(x) and the initial condition y(π) = 1. (5 points) 


2. 
The slope of the tangent to a curve at any point (x, y) on the curve is . Find the equation of the curve if the point (2, 2) is on the curve. (5 points) 
x + y = 0 x2 – y2 = 2 x2 + y2 = 16 x2 + y2 = 8 
3. 
The rate of decay in the mass, M, of a radioactive substance is given by the differential equation , where k is a positive constant. If the initial mass was 150g, then find the expression for the mass, M, at any time t. (5 points) 
M = ekt M = 150 ekt M = 150 ekt M = 150ln(kt) 
4. 
The temperature of a cup of hot tea varies according to Newton’s Law of Cooling: , where T is the temperature of the tea, A is the room temperature, and k is a positive constant. If the water cools from 100°C to 80°C in 1 minute at a room temperature of 60°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes. (5 points) 
42 58 63 79 
5. 
The differential equation (5 points) I.produces a slope field with horizontal tangents at x = 4 
I only II only I and II II and III only 
6. 
Which of the following differential equations is consistent with the following slope field? (5 points) 
7. 
The general solution of the differential equation x dx – y dy = 0 is a family of curves. These curves are all (5 points) 
hyperbolas circles parabolas ellipses 
8. 
Estimate the value of by using the Trapezoidal Rule with n = 3. (5 points) 
252 128 63 72 
9. 
The table below gives selected values for the function f(x). With 5 rectangles, using the left side of each rectangle to evaluate the height of each rectangle, estimate the value of . (5 points) x 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 f(x) 1 0.909 0.833 0.769 0.714 0.667 0.625 0.588 0.556 0.526 0.500 
0.7456 0.6456 0.6919 0.6932 
10. 
Given f(x) > 0 with f ′ (x) > 0, and f ″(x) > 0 for all x in the interval [0, 3] with f(0) = 0.1 and f(3) = 1, the left, right, trapezoidal, and midpoint rule approximations were used to estimate . The estimates were 0.8067, 0.9635, 1.0514, 1.0753 and 1.3439, and the same number of subintervals were used in each case. Match the rule to its estimate. (5 points) 
____ 1. left endpoint ____ 2. right endpoint ____ 3. midpoint ____ 4. trapezoidal ____ 5. actual area a. 1.0753 b. 0.9635 c. 1.0514 d. 1.3439 e. 0.8067 

11.

The graph of f ′(x) is continuous and decreasing with an xintercept at x = 0. Which of the following statements is true? (4 points) 
The graph of f has a relative maximum at x = 0. The graph of f has a relative minimum at x = 0. The graph of f has an inflection point at x = 0. The graph of f has an xintercept at x = 0. 
12. 
The graph below shows the graph of f (x), its derivative f ′(x), and its second derivative f ″(x). Which of the following is the correct statement? (4 points) 
A is f ″, B is f ′, C is f. A is f ″, B is f, C is f ′. A is f ′, B is f, C is f ″. A is f, B is f ′, C is f ″. 
13. 
Below is the graph of f ′(x), the derivative of f(x), and has xintercepts at x = 3, x = 1 and x = 2. There are horizontal tangents at x = 1.5 and x = 1.5. Which of the following statements is true? (4 points) 
f has an inflection point in the interval x = 1 to x = 1. f is increasing on the interval from x = 3 to x = 1. f has a relative maximum at x = 1.5. None of these is true. 
14. 
The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 7, find the absolute minimum value of f (x) over the interval [3, 0]. (4 points) 
0 2.5 4.5 11.5 
15. 
The graph of y = f ′(x), the derivative of f(x), is shown below. Given f(4) = 2, evaluate f(4). (4 points) 
0 2 8 10 
16. 
Which of the following functions grows the fastest as x goes to infinity? (4 points) 
2x ln(x) sin(x) x20 
17. 
Compare the rates of growth of f(x) = and g(x) = Ln(x) as x approaches infinity. (4 points) 
f(x) grows faster than g(x) as x goes to infinity. g(x) grows faster than f(x) as x goes to infinity. f(x) and g(x) grow at the same rate as x goes to infinity. The rate of growth cannot be determined. 
18. 
What does show? (4 points) 
g(x) grows faster than f(x) as x goes to infinity. f(x) and g(x) grow at the same rate as x goes to infinity. f(x) grows faster than g(x) as x goes to infinity. L’Hôpital’s Rule must be used to determine the true limit value. 
19. 
Which of the following functions grows at the same rate as ? (4 points) 
x x2 x3 x4 
20. 
Which of the following functions grows the slowest as x goes to infinity? (4 points) 
5x 5x x5 They all grow at the same rate. 
21. 
The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Use the data in the table to approximate f ′(12). (4 points) x 3 4 7 11 13 f(x) 2 8 10 12 22

22. 
f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives values of f ‘(x). What is the value of g ‘(0.1)? (4 points) x 0.1 0.2 0.3 0.4 0.5 f ‘(x) 1 2 3 4 5 
16 4 4 Cannot be determined 
23. 
f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f ‘(x), and g ‘(x). Find the value of h ‘(1). (4 points) x 1 2 3 4 5 6 f(x) 0 3 2 1 2 0 g(x) 1 3 2 6 5 0 f ‘(x) 3 2 1 4 0 2 g ‘(x) 1 5 4 3 2 0 
24. 
The table of values below shows the rate of water consumption in gallons per hour at selected time intervals from t = 0 to t = 12. Using a right Riemann sum with 5 subintervals estimate the total amount of water consumed in that time interval. (4 points) x 0 2 5 7 11 12 f(x) 5.7 5.0 2.0 1.2 0.6 0.4 
2.742 21.2 32.9 None of these 
25. 
The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Right Hand Sum Approximation, using the intervals between those given points. (4 points) x 10 12 15 19 20 f(x) 2 5 9 12 16 
9.250 10.100 7.550 6.700 

26. 
Let . Use your calculator to find F”(1). (4 points) 
5.774 11.549 18.724 37.449 
27. 
Cleaning pumps remove oil at the rate modeled by the function R, given by with t measure in hours and and R(t) measured in gallons per hour. How much oil will the pumping stations remove during the 6hour period from t = 0 to t = 6? Give 3 decimal places. (4 points) 
28. 
A particle moves along the xaxis with velocity v(t) = t2 – 1, with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = 2 seconds. (4 points) 
0.667 2 4 None of these 
29. 
Find the range of the function . (4 points) 
[4, 4] [4, 0] [0, 4π] [0, 8π] 
30. 
Use the graph of f(t) = 2t + 3 on the interval [3, 6] to write the function F(x), where . (4 points) 
F(x) = 2×2 + 6x F(x) = 2x + 3 F(x) = x2 + 3x + 54 F(x) = x2 + 3x – 18 
SHOW WORK (15)
1.
Write and then solve for y = f(x) the differential equation for the statement: “The rate of change of y with respect to x is inversely proportional to y4.”
_________________________________
2.
Solve the differential equation for y = f(x) with the condition y(1) = 1.
_________________________________
3.
1. Solve the differential equation .
_________________________________
2. b. Explain why the initial value problem with y(0) = 4 does not have a solution.
_________________________________
4.
The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of . Give 3 decimal places for your answer. (10 points)
x
1
1.1
1.3
1.6
1.7
1.8
2.0
f(x)
1
3
5
8
10
11
14
_________________________________
5.
Using 4 equalwidth intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for . (10 points)
_________________________________
cos(x)
2 – cos(x)
1 – cos(x)
1 – cos(x)
1.

Find the particular solution to y ‘ = sin(x) given the general solution is y = C – cos(x) and the initial condition . (5 points) 

2. 
The slope of the tangent to a curve at any point (x, y) on the curve is . Find the equation of the curve if the point (2, 2) is on the curve. (5 points) 

x + y = 0 x2 – y2 = 2 x2 + y2 = 16 x2 + y2 = 8 
3. 
The rate of decay in the mass, M, of a radioactive substance is given by the differential equation , where k is a positive constant. If the initial mass was 200g, then find the expression for the mass, M, at any time t. (5 points) 

M = 200ln(kt) M = 2ekt M = 200 ekt M = 200 ekt 
4. 
The temperature of a cup of hot tea varies according to Newton’s Law of Cooling: , where T is the temperature of the tea, A is the room temperature, and k is a positive constant. If the water cools from 100°C to 80°C in 1 minute at a room temperature of 60°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes. (5 points) 

42 58 63 79 
5. 
The differential equation (5 points) I.produces a slope field with horizontal tangents at y = 2 

I only II only I and II III only 
6. 
Which of the following differential equations is consistent with the following slope field? (5 points) 
7. 
The general solution of the differential equation dy – 0.2x dx = 0 is a family of curves. These curves are all (5 points) 
lines hyperbolas parabolas ellipses 
8. 
Estimate the value of by using the Trapezoidal Rule with n = 4. (5 points) 
8 19 22 36 
9. 
The table below gives selected values for the function f(x). With 5 rectangles, using the left side of each rectangle to evaluate the height of each rectangle, estimate the value of . (5 points) x 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 f(x) 1 0.909 0.833 0.769 0.714 0.667 0.625 0.588 0.556 0.526 0.500 
0.7456 0.6456 0.6919 0.6932 
1.
10. 
Given f(x) > 0 with f ′(x) < 0, and f ″(x) > 0 for all x in the interval [0, 2] with f(0) = 1 and f(2) = 0.2, the left, right, trapezoidal, and midpoint rule approximations were used to estimate . The estimates were 0.7811, 0.8675, 0.8650, 0.8632 and 0.9540, and the same number of subintervals were used in each case. Match the rule to its estimate. (5 points) 
abcde 1. left endpoint abcde 2. right endpoint abcde 3. midpoint abcde 4. trapezoidal abcde 5. actual area a. 0.7811 b. 0.8650 c. 0.8675 d. 0.9540 e. 0.8632 

Which of the following functions grows the fastest as x goes to infinity? (4 points) 

2x 3x ex x20 
Compare the rates of growth of f(x) = and g(x) = Ln(x) as x approaches infinity. (4 points) 
f(x) grows faster than g(x) as x goes to infinity. g(x) grows faster than f(x) as x goes to infinity. f(x) and g(x) grow at the same rate as x goes to infinity. The rate of growth cannot be determined. 
What does show? (4 points) 
g(x) grows faster than f(x) as x goes to infinity. f(x) and g(x) grow at the same rate as x goes to infinity. f(x) grows faster than g(x) as x goes to infinity. L’Hôpital’s Rule must be used to determine the true limit value. 
Which of the following functions grows at the same rate as ? (4 points) 
x x2 x3 x4 
Which of the following functions grows the slowest as x goes to infinity? (4 points) 
5x 5x x5 They all grow at the same rate. 
Let . Use your calculator to find F”(1). (4 points) 
12 6 4 
Pumping stations deliver gasoline at the rate modeled by the function D, given by with t measure in hours and and R(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 3hour period from t = 0 to t = 3? Give 3 decimal places. (4 points) 
A particle moves along the xaxis with velocity v(t) = sin(2t), with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = π seconds. (4 points) 
2 1 0 
Find the range of the function . (4 points) 
[4, 4] [4, 0] [0, 4π] [0, 8π] 
Use the graph of f(t) = 2t + 4 on the interval [4, 6] to write the function F(x), where . (4 points) 
F(x) = x2 + 6x F(x) = x2 + 4x – 12 F(x) = x2 + 4x – 8 F(x) = x2 + 8x – 20 
Topquality papers guaranteed
100% original papers
We sell only unique pieces of writing completed according to your demands.
Confidential service
We use security encryption to keep your personal data protected.
Moneyback guarantee
We can give your money back if something goes wrong with your order.
Enjoy the free features we offer to everyone

Title page
Get a free title page formatted according to the specifics of your particular style.

Custom formatting
Request us to use APA, MLA, Harvard, Chicago, or any other style for your essay.

Bibliography page
Don’t pay extra for a list of references that perfectly fits your academic needs.

24/7 support assistance
Ask us a question anytime you need to—we don’t charge extra for supporting you!
Calculate how much your essay costs
What we are popular for
 English 101
 History
 Business Studies
 Management
 Literature
 Composition
 Psychology
 Philosophy
 Marketing
 Economics