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#1 2013-06-24 22:44:46

ShivamS
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Tangent Vector practice problems

Please check the following.

Vector r = (e^3t, sin(2t), t^2)


What is vector r(t) prime? I am getting (3e^3t, 2cos(2t), 2t)

Compute the unit tangent vector T(t) and do not simplify the answer. I get vector T(t) = (3e^3t, 2cos(2t), 2t) divided by square root of (9e^6t + 4cos^2(2t) +4t^2)

Thanks in advance.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#2 2013-06-24 23:06:47

anonimnystefy
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Re: Tangent Vector practice problems

That look correct! smile


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-06-24 23:41:33

ShivamS
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Re: Tangent Vector practice problems

Thanks a lot.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#4 2013-06-25 00:34:15

anonimnystefy
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Re: Tangent Vector practice problems

You're welcome.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#5 2013-06-25 00:52:04

ShivamS
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Re: Tangent Vector practice problems

More stuff: g(t) = 4t+1  what is d/dt r(g9t))

I get 4{3e^3(4t+1), 2cos[2(4t+1)], 2(4t+1)}


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#6 2013-06-25 02:24:41

bob bundy
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Re: Tangent Vector practice problems

hi

r(g9t)) I take it that's r(g(t)) so chain rule

dr/dt = dr/dg x dg/dt

Take the first component.  I'm thinking that is



Or am, I mixing up here?

so

diff gives





Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#7 2013-06-25 02:26:29

ShivamS
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Re: Tangent Vector practice problems

d/dt r(g(t)) = g'(t)r'(g(t)) = d/dt(4t+1)r'(4t+1)


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#8 2013-06-25 02:27:05

anonimnystefy
Real Member

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Re: Tangent Vector practice problems

Hi Shivamcoder3013

I would say that is correct as well.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#9 2013-06-25 02:27:40

bob bundy
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Re: Tangent Vector practice problems

Sorry I put an edit in above.

Please look.  smile

Back later

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#10 2013-06-25 02:28:49

ShivamS
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Re: Tangent Vector practice problems

Thanks.

Last edited by Shivamcoder3013 (2013-06-25 02:28:56)


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#11 2013-06-25 03:31:03

bob bundy
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Re: Tangent Vector practice problems

hi Shivamcoder3013

Your notation is confusing me.  I'd do this like this:





Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#12 2013-06-25 07:42:13

ShivamS
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Re: Tangent Vector practice problems

That is not different from my answer.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#13 2013-06-25 17:14:18

bob bundy
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Re: Tangent Vector practice problems

hi Shivamcoder3013

Oh, that's a big relief for me.  Somehow, I missed that.  Sorry I've dragged this thread out longer than was necessary  smile

Bob.


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

#14 2013-06-27 09:59:14

ShivamS
Super Member

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Re: Tangent Vector practice problems

No problem. Thanks both of you.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

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