Assignment 2-5

course MTH 174

捭藤顦y嗙ⅹ娌更爙腙鷞諣繿ssignment #002

嚚澏蓛媫槵翴品烍米wx耹欄�

Physics II

06-28-2008

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20:22:51

What is the solution satisfying the given initial condition?

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RESPONSE -->

s= -16t^2+100t+50

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20:23:20

What is the general solution to the differential equation?

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RESPONSE -->

-16t^2+100t+C

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20:25:58

How fast is the water balloon moving when it strikes the ground?

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RESPONSE -->

3.104 seconds

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20:26:04

How fast is the water balloon moving when it strikes the 6 ft person's head?

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RESPONSE -->

3 seconds

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20:26:19

What is the average velocity of the balloon between the two given clock times?

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RESPONSE -->

-32 feet per second

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20:26:42

What function describes the velocity of the balloon as a function of time?

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RESPONSE -->

v(t) = -32t+40

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20:27:13

What is the desired derivative?

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RESPONSE -->

-ln(x)

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20:28:34

The Second Fundamental Theorem applies to an integral whose upper limit is the variable with respect to which we take the derivative. How did you deal with the fact that the variable is the lower limit?

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RESPONSE -->

F(b)-F(a) = t*ln(t)-t

d/dx(t*ln(t)-t)

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20:28:46

Why do we use something besides x for the integrand?

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RESPONSE -->

?

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20:29:21

What is the desired derivative?

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RESPONSE -->

sin(x)*e^((cos(x))^2)

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assignment #003

嚚澏蓛媫槵翴品烍米wx耹欄�

Physics II

06-28-2008

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20:29:57

query 6.5 #8 Galileo: time for unif accel object to traverse dist is same as if vel was ave of init and final; put into symbols and show why true

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RESPONSE -->

?

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20:32:12

what did you get for the integral and how did you reason out your result?

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RESPONSE -->

u= cos(3t), du= -sin(3t)dt

the negative intergral of u^(1/2)du

= (2*cos(3t)^(3/2))/3 + C

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20:32:55

what is the antiderivative?

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RESPONSE -->

(e^(x^3+1))/3 + C

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20:33:31

What substitution would you use to find this antiderivative?

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RESPONSE -->

e^u*du

u=x^3+1

du = 3x^2dx

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20:34:21

what is the antiderivative?

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RESPONSE -->

2*ln(abs(t)) - 1/t +t + C

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20:36:10

What substitution would you use to find this antiderivative?

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RESPONSE -->

I broke the integral down into 3 seperate integrals.

the integral of 1/t^2*dt

plus

the integral of 2/tdt

plus

the integral of 1*dt

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20:36:25

What did you get for the definite integral?

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RESPONSE -->

1/40

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20:37:14

What antiderivative did you use?

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RESPONSE -->

the integral of u^-2 du

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20:38:29

What is the value of your antiderivative at t = 1 and at t = 3?

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RESPONSE -->

t(1) = 1/8

t(3) = -1/10

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20:39:15

What were the populations in 1990 and 2000?

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RESPONSE -->

1990 - 5.3 billion

2000 - 6.096 billion

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20:39:39

What is the average population between during the 1990's and how did you find it?

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RESPONSE -->

5.67 billion, I added the 10 years together and divided by 10?

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20:39:48

What is the value of your antiderivative at t = 1 and at t = 3?

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RESPONSE -->

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20:39:50

Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

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assignment #004

嚚澏蓛媫槵翴品烍米wx耹欄�

Physics II

06-28-2008

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20:42:54

what is the requested antiderivative?

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RESPONSE -->

(-cos(theta)*sin(theta)+theta)/2

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20:44:18

What substitution, breakdown into parts and/or other tricks did you use to obtain the antiderivative?

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RESPONSE -->

u= sin(theta)

du = cos(theta)*d(theta)

dv= sin(theta)*d(theta)

v = -cos(theta)

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20:45:23

what is the requested antiderivative?

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RESPONSE -->

(2(3t+2)^(3/2)*(9t+26))/135

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20:46:23

What substitution, breakdown into parts and/or other tricks did you use to obtain the antiderivative?

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RESPONSE -->

u= t+2

du= dt

dv= (2+3t)^(1/2)dt

v= (2(3t+2)^(3/2))/9

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20:46:34

query problem 7.2.27 antiderivative of x^5 cos(x^3)

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RESPONSE -->

?

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20:46:55

What is the value of the requested integral?

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RESPONSE -->

-9

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20:48:23

How did you use integration by parts to obtain this result? Be specific.

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RESPONSE -->

u= x

du= dx

dv= f''(x)dx

v= f'(x)

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assignment #005

嚚澏蓛媫槵翴品烍米wx耹欄�

Physics II

06-28-2008

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22:39:08

what it is your antiderivative?

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RESPONSE -->

= e^(3x)*((x^4/3) - (4x^3/9) + (4x^2/9) - (8x/27) + (8/81)) + C

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22:39:35

Which formula from the table did you use?

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RESPONSE -->

the integral of p(x)*e^(ax)dx

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22:40:57

You should have used formula 14. What was your value of a, what was p(x), how many derivatives did you use and what were your derivatives of p(x)?

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RESPONSE -->

a= 3

p(x)= x^4

I used four(4) derivatives.

4x^3

12x^2

24x

24

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22:42:03

What is your integral?

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RESPONSE -->

(tan(z+2))^-1 + C

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22:43:15

Which formula from the table did you use and how did you get the integrand into the form of this formula?

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RESPONSE -->

the integral of 1/(x^2 + a^2)

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23:34:32

7.4.6 (#8 in 3d edition). Integrate 2y / ( y^3 - y^2 + y - 1)

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RESPONSE -->

1/(y-1) + (1-y)/(y^2+1)

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23:36:39

What substitution did you use?

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RESPONSE -->

the integral of (z-1)/sqrt(-(z-1)^2+1)

z= (3sec(theta))/2

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23:40:54

What is your integral and how did you obtain it?

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RESPONSE -->

A/(2y+1) + B/(y+1)

A(y+1) + B(2y+1) = y+2

y= -1 -> 0 + B(2(-1)+1) = -1+2

B= -1

y= (-1/2) -> A(1/2) + 0 = 3/2

A= 3

this gives the integral of (3/(2y+1)) - (1/(y+1))

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"

Your work looks good overall, though you need some feedback on at least a few of these problems. I can't give you feedback based on this document, but you can remedy that fairly easily.

Your document skips a lot of information. I could follow your work here by referring to another document, but that takes much more time than going through a single document. In most cases I can't tell from this document what question is being answered.

I'm going to have to ask you to insert your responses into a full document. This will require that you 'click through' the queries in the sequence described below, and insert your answers at the appropriate places. This shouldn't take you too long, and it will give me a document I can analyze. If you are very sure of a solution, then you can just leave it out, but be sure to include responses to anything you aren't 100% sure of.

&#Describe your sketch. Your description does a better job of indicating what you do and do not understand than would a sketch. &#