assignment 8

#$&*

course MTH 277

7/1/13

Assignment 8If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

At the end of this document, after the qa problems (which provide you with questions and solutions), there is a series of Questions, Problems and Exercises.

query_10_1

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Question: Find the domain of F(t) X G(t) when F(t) = t^2 i - (t+2)j + (t-1)k and G(t) = (1/(t+2))i + (t-5)j + sqrt(t) k.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The cross product of the F(t) and G(t) is

t^.5(-t-2)-(t-1)(t-5) i hat, t^2.5-(t-1)/(t+2) j hat, t^3-5t^2+(t-2)/(t+2)

so t cannot be less than 0. T cannot be -2.

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):ok

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Self-critique rating:ok

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Question: Describe the graph of G(t) = (sin t)i + (cos t)j + (4/3)k

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

In the x-y graph it will be a sin wave determining x and a cos wave determining y. Z will always be 4/3.

@&
sin(t) vs. t is a sine wave, as is cos(t) vs. t, the latter being 90 degrees out of phase with the former.

However

sin(t) `i + cos(t) `j

describes a circle.
*@

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):ok

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Self-critique rating:ok

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Question: Given F(t)= (t)i - 5(e^t)j +(t^3)k, G(t) = ti - (1/t)k and H(t) = (t*sin t)i + (e^-t)j, find H(t) dot [G(t) X F(t)]

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

GxF

=5t^-1e^t,t^4-1,5te^t

H. ans=

5e^tsint+e^-t(t^4-1)

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):ok

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Self-critique rating:ok

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Question: Find a vector function F whose graph is the curve given by the equation x/5 = (y-3)/6 = (z+2)/4.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

12x=10y=15z+6

@&
This is not a vector function.

A vector function `F would be

`F(t) = x(t) `i + y(t) `j + z(t) `k

You would need to express the function in this form, specifying the functions x(t), y(t) and z(t).
*@

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):ok

------------------------------------------------

Self-critique rating:ok

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Question: Find the limit as t -> 2 of ((t^4-2)/(t-2))i + ((t^2-4)/(t^2-2t))j + ((t^2 + 3)e^(t-2))k.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

For i infinity

J, use L’Hospital

(4+3)e^0=7 for K.

confidence rating #$&*:ot sure about i.

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:ok

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Question: How many revolutions are made by the circular helix R(t) = (sin t)i + (cos t)j + (3/4)tk in a vertical distance of 12 units.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution: I looked online and found that circular helixes have the form

a⋅cos(t)i+a⋅sin(t)j+ctk.

@&

Note also that if you copy and pasted into a word processor instead of a text editor you're likely to get a lot of meaningless expressions like #8901.
*@

@&

@&
A formula from the Internet can be useful to check yourself, but it isn't otherwise likely to help you understand vector functions.

You need to understand why sin(t) `i + cos(t) `j is a circle, and how the addition of (3/4) t `k makes it into a helix.

The references I provided to some of my Precalculus II materials address parametric equations and conic sections, as do a number of Internet resources (e.g., Khan Academy).
*@

Does this matter if the sin and cos are switched in the question.

@&
Based on your knowledge of the sine and cosine functions, and parametric equations, you should be able to determine how this changes the function and whether it matters for the present question.
*@

Use arc length formula

L=int from 0 to s sqrt(sin^2(t)+cos^2(t)+9/16)dt=12 find that int 0 to s of 5/4dt=12 5s/4=12 s=48/5

@&

@&
It's good to be able to deal with this arc length, but it won't help you determine the number of revolutions.

The question doesn't ask about arc length 12, it asks about vertical distance 12.

Your integral and your results do correctly address quantities relevant to arc length 12.
*@

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

#*&!

@&
Not bad, but I do suggest a little more review of some of the prerequisites, in order to better understand these vector functions.

Check my notes.
*@

assignment 8

@& sin(t) vs. t is a sine wave, as is cos(t) vs. t, the latter being 90 degrees out of phase with the former. However sin(t) `i + cos(t) `j describes a circle. *@

@& This is not a vector function. A vector function `F would be `F(t) = x(t) `i + y(t) `j + z(t) `k You would need to express the function in this form, specifying the functions x(t), y(t) and z(t). *@

@& Note also that if you copy and pasted into a word processor instead of a text editor you're likely to get a lot of meaningless expressions like #8901. *@

@&

@& Based on your knowledge of the sine and cosine functions, and parametric equations, you should be able to determine how this changes the function and whether it matters for the present question. *@

@&

@& It's good to be able to deal with this arc length, but it won't help you determine the number of revolutions. The question doesn't ask about arc length 12, it asks about vertical distance 12. Your integral and your results do correctly address quantities relevant to arc length 12. *@

@& Not bad, but I do suggest a little more review of some of the prerequisites, in order to better understand these vector functions. Check my notes. *@

@&
sin(t) vs. t is a sine wave, as is cos(t) vs. t, the latter being 90 degrees out of phase with the former.

However

sin(t) `i + cos(t) `j

describes a circle.
*@

@&
This is not a vector function.

A vector function `F would be

`F(t) = x(t) `i + y(t) `j + z(t) `k

You would need to express the function in this form, specifying the functions x(t), y(t) and z(t).
*@

@&

Note also that if you copy and pasted into a word processor instead of a text editor you're likely to get a lot of meaningless expressions like #8901.
*@

@&
Based on your knowledge of the sine and cosine functions, and parametric equations, you should be able to determine how this changes the function and whether it matters for the present question.
*@

@&
It's good to be able to deal with this arc length, but it won't help you determine the number of revolutions.

The question doesn't ask about arc length 12, it asks about vertical distance 12.

Your integral and your results do correctly address quantities relevant to arc length 12.
*@

@&
Not bad, but I do suggest a little more review of some of the prerequisites, in order to better understand these vector functions.

Check my notes.
*@