Calc HW
flcoman89
calchw5.pdf
Kyle Taitt CSU Webwork
MATH 160 WeBWorK assignment M160-801-FA-2.4 due 10/04/2016 at 11:59pm MDT
1. (1 point) If f (y) = tan(5y), then f 00(y) is
Answer(s) submitted:
•
(incorrect)
2. (1 point) Let f (x) = 1�4x1+4x . Compute the following.
f
0(4) = f
00(4) = f
000(4) = Answer(s) submitted:
• • •
(incorrect)
3. (1 point) If g(t) = 2t 4 + 8t 2 + 5 find
g(0) =
g
0(0) =
g
00(0) =
g
000(0) =
g
(4)(0) =
g
(5)(0) =
Answer(s) submitted:
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(incorrect)
4. (1 point) d
4
dx
4
✓ �8x4
1 � x
◆ =
Note: There is a way of doing this problem without using the quotient rule 4 times.
Answer(s) submitted:
•
(incorrect)
5. (1 point) Find the 75th derivative of sin(x) by finding the first few derivatives and observing the pattern that occurs. (sin(x))(75) =
Answer(s) submitted:
• (incorrect)
6. (1 point) Let f (x) = p
x
2 + 3.
f
0(x) =
f
0(4) = ,
f
00(x) =
f
00(4) = Answer(s) submitted:
• • • •
(incorrect)
7. (1 point)
Identify the graphs B (blue), R (red) and G (green) as the graphs of a function and its derivatives: (Note- you can click on the graph to view a larger version.)
is the graph of the function is the graph of the function’s first derivative is the graph of the function’s second derivative
Answer(s) submitted:
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1
(incorrect) 8. (1 point) A particle moves along a straight line and its
position at time t is given by s(t) = 2t 3 � 21t 2 + 36t where s is measured in feet and t in seconds. Find the velocity (in ft/sec) of the particle at time t = 0:
The particle stops moving (i.e. is in a rest) twice, once when t = A and again when t = B where A < B. A is and B is What is the position of the particle at time 14?
Finally, what is the TOTAL distance the particle travels between time 0 and time 14?
Answer(s) submitted:
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(incorrect) 9. (1 point) A particle moves along a straight line with equa-
tion of motion s = t 5 � 4t 4 Find the value of t (other than 0 ) at which the acceleration is equal to zero.
Answer(s) submitted:
• (incorrect)
10. (1 point) Let s(t) give the position of a moving body where s is in meters and t is in seconds. Find the following at time t = p/3. Let s(t) = �2 + cos(t). The velocity is The speed is The acceleration is The jerk is
Answer(s) submitted:
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(incorrect) 11. (1 point) The quantity of charge Q in coulombs (C) that has passed
through a point in a wire up to time t (measured in seconds) is given by Q(t) = t 3 � 2t 2 + 6t + 2 + 4. Find the current when: (a) t = .5 sec (b) t = 1 sec
The unit of current is an ampere (1 A = 1 C/s). (a) A
(b) A
Answer(s) submitted:
• •
(incorrect)
12. (1 point) If a tank holds 1000 gallons of water, which drains from the
bottom of the tank in 40 minutes, then Torricelli’s Law gives the volume V of water remaining in the tank after t minutes as
V = 1000 ⇣
1 � t
40
⌘2 0 t 40.
Find the rate at which the water is draining out of the tank after: (a) 5 min (b) 10 min (c) 20 min (d) 40 min
(a) gal/min (b) gal/min (c) gal/min (d) gal/min
Answer(s) submitted:
• • • •
(incorrect)
13. (1 point) The graph shows the position function of a car. Use the shape of the graph to answer the following questions.
a. What was the initial velocity of the car?
Answer:
b. Was the car going faster at B or at C? [Enter the appro- priate letter.]
Answer:
c. What was the velocity of the car between D and E?
Answer:
Answer(s) submitted:
• • •
(incorrect)
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14. (1 point) The figure shows the graphs of three functions. One is the
position function (s) of a car, one is the velocity (v) of a car, and one is its acceleration (a). Identify each curve.
s : v : a :
Answer(s) submitted:
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(incorrect) 15. (1 point) Suppose that the equation of motion for a parti-
cle (where s is in meters and t in seconds) is
s = sin(4pt) . (a) Find the velocity and acceleration as functions of t.
Velocity at time t = Acceleration at time t =
(b) Find the acceleration after 1 second. Acceleration after 1 second:
(c) Find the acceleration (in absolute value) at the instant when the velocity is 0.
Acceleration:
Answer(s) submitted:
• • • •
(incorrect) 16. (1 point) Calculate the derivative indicated.
d
2 y
dx
2
���� x=6
where y = 3x�3 + 9x2
Answer: Answer(s) submitted:
• (incorrect)
17. (1 point) Find d
69
dx
69 sin(2x). Answer: Answer(s) submitted:
• (incorrect)
18. (1 point) Two perpendicular lines intersect the y-axis at the same point and are tangent to the parabola y = x2. Where do these lines intersect?
x = y = Answer(s) submitted:
• •
(incorrect)
19. (1 point) A space traveler is moving from left to right along the curve
y = x2.
When she shuts off the engines, she will continue traveling along the tangent line at the point where she is at that time. At what point
(x,y) = ( , )
should she shut off the engines in order to reach the point (4,15)?
If she was traveling from right to left she would have to shut off the engines at the point
(x,y) = ( , ). Answer(s) submitted:
• • • •
(incorrect)
20. (1 point) Determine coefficients a and b such that p(x) = x2 + ax + b satisfies p(1) = 5 and p0(1) = �3.
a =
b = Answer(s) submitted:
• •
(incorrect)
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