Calculus. Again.

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Calculus. Again.

Postby Mangafanatic » Wed Nov 08, 2006 6:01 pm

So, yeah. I hate this stuff. :(

Anyways, guys, I am so confused. Right now, we're talking about implicit differentiation, and I'm completely lost. The problem I'm trying to work through is 2^2+[square root of (st)]+2t^3-5t=0. I'm supposed to find velocity ds/dt. How on earth do I do that? 0__o Please, help me, someone.
Every year in Uganda, innumerable children simply. . . disappear. These children all stolen under the cover of darkness from their homes and impressed into the guerilla armies of the LRA [Lord's Resistance Army]. In the deserts of Uganda, they are forced to witness the mindless slaughter of other children until they themselves can do nothing but kill. Kill. These children, generally ranging from ages 5-12, are brainwashed into murdering in the name of the resistance and into stealing other children from their beds to suffer the same fate.

Because of this genocide of innocence, hundred and hundreds of children live every night sleeping in public places miles from their homes, because they know that if the do not-- they will disappear. They will become just another number in this genocide to which the international community has chosen to turn a blind eye. They will become, in affect, invisible-- Invisible Children.

But there are those who are trying to fight against this slaughter of Uganda's children. They fight to protect these "invisible children." Please, help them help a country full of children who know nothing by fear. Help save the innocence. For more information concerning how you can help and how you can get an incredible video about this horrific reality, visit the Invisible Children home page.
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Postby Puritan » Wed Nov 08, 2006 6:30 pm

Yay calculus! :P

If you take the problem and differentiate by t it becomes:

(4+(st)^(1/2)+t^3-5t)dt=0dt

which becomes (using the product rule)

(1/2)*(st)^(-1/2)*(t*(ds/dt)+s))+3t^2-5=0

solving for ds/dt you get

ds/dt=(3*t^2-5*(st)^(1/2))*2+s

now you just need to solve the original equation for s (using algebra) and plug that solution into this equation. It's going to be a bit messy, but from this point on it's more messy algebra than any difficult calculus

Now, if you're confused about the product rule (i.e. if you have to differentiate two things multiplied by each other) it goes like this:

d(u*v)/dx=du/dx*v+dv/dx*u

Also, you could be having problems with differentiating (s*t)^1/2. In that case, the rule is d((u*v)^w)/dx = d(y^w)/dx where y=u*v. d(y^w)/dx = w*(y^(w-1))*dy/dx

I hope that helps! I'd be happy to try to give you more advice, but I think you can take it from here.
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Postby Mithrandir » Wed Nov 08, 2006 7:08 pm

O.O

29 minutes. Wow Puritan. Just... Wow.
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Postby Mangafanatic » Wed Nov 08, 2006 7:10 pm

That does help. Except I screw up. The equation was actually 2s^2+[the square root of (st)]-4=3t

Sorry!
Every year in Uganda, innumerable children simply. . . disappear. These children all stolen under the cover of darkness from their homes and impressed into the guerilla armies of the LRA [Lord's Resistance Army]. In the deserts of Uganda, they are forced to witness the mindless slaughter of other children until they themselves can do nothing but kill. Kill. These children, generally ranging from ages 5-12, are brainwashed into murdering in the name of the resistance and into stealing other children from their beds to suffer the same fate.

Because of this genocide of innocence, hundred and hundreds of children live every night sleeping in public places miles from their homes, because they know that if the do not-- they will disappear. They will become just another number in this genocide to which the international community has chosen to turn a blind eye. They will become, in affect, invisible-- Invisible Children.

But there are those who are trying to fight against this slaughter of Uganda's children. They fight to protect these "invisible children." Please, help them help a country full of children who know nothing by fear. Help save the innocence. For more information concerning how you can help and how you can get an incredible video about this horrific reality, visit the Invisible Children home page.
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Postby Yumie » Wed Nov 08, 2006 7:20 pm

Mangafanatic wrote:That does help. Except I screw up. The equation was actually 2s^2+[the square root of (st)]-4=3t

Sorry!


Oh wow. I think Osaka needs a proof-reading tutorial instead of a calculus one. That's terrible.
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Be Thou my Wisdom, and Thou my true Word;
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Thou in me dwelling, and I with Thee one.

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Postby Mangafanatic » Wed Nov 08, 2006 8:00 pm

Yumie wrote:Oh wow. I think Osaka needs a proof-reading tutorial instead of a calculus one. That's terrible.


Hey. No picking on me. I've been working on Calculus for 2 hours and I've gotten NOTHING done. Yeah. I'm somewhat. . . irked.
Every year in Uganda, innumerable children simply. . . disappear. These children all stolen under the cover of darkness from their homes and impressed into the guerilla armies of the LRA [Lord's Resistance Army]. In the deserts of Uganda, they are forced to witness the mindless slaughter of other children until they themselves can do nothing but kill. Kill. These children, generally ranging from ages 5-12, are brainwashed into murdering in the name of the resistance and into stealing other children from their beds to suffer the same fate.

Because of this genocide of innocence, hundred and hundreds of children live every night sleeping in public places miles from their homes, because they know that if the do not-- they will disappear. They will become just another number in this genocide to which the international community has chosen to turn a blind eye. They will become, in affect, invisible-- Invisible Children.

But there are those who are trying to fight against this slaughter of Uganda's children. They fight to protect these "invisible children." Please, help them help a country full of children who know nothing by fear. Help save the innocence. For more information concerning how you can help and how you can get an incredible video about this horrific reality, visit the Invisible Children home page.
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Postby Warrior4Christ » Wed Nov 08, 2006 8:59 pm

Mangafanatic wrote:That does help. Except I screw up. The equation was actually 2s^2+[the square root of (st)]-4=3t

Sorry!

Yeah, sure. That was just the next question! :P

2*2(s ^1) * ds/dt + 1/2*(st)^(-1/2) * (ds/dt * t + s * dt/dt) = 3*dt/dt

=> 4s * ds/dt + (ds/dt *t + s)/(2 * (st) ^ (1/2) = 3

The rest is left as an exercise for the reader.
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Postby Mithrandir » Wed Nov 08, 2006 9:29 pm

Warrior4Christ wrote:Yeah, sure. That was just the next question! :P

:lol:

She wouldn't do that. She's a good girl. Well, except for that time with the limo and the robot-hampster. I *still* can't get the ketchup stains out of my tux.
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Postby Icarus » Wed Nov 08, 2006 10:18 pm

Warrior4Christ wrote:The rest is left as an exercise for the reader.

Classic.
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Postby Puritan » Thu Nov 09, 2006 6:27 pm

Mithrandir wrote:O.O

29 minutes. Wow Puritan. Just... Wow.



*looks left* *looks right* Can you keep a secret?
...
...
For some odd reason, I really love calculus. I can't explain it, but I really like it. When I saw this post I was oddly thrilled to be able to help someone solve a calculus problem. I admit, I'm a nutty engineer, but at least I'm easy to please...
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Postby Yumie » Thu Nov 09, 2006 9:10 pm

Puritan wrote:*looks left* *looks right* Can you keep a secret?
...
...
For some odd reason, I really love calculus. I can't explain it, but I really like it. When I saw this post I was oddly thrilled to be able to help someone solve a calculus problem. I admit, I'm a nutty engineer, but at least I'm easy to please...


So, when I take calculus next year, I know who go to to ask questions. . .

YUS!!! :dance:
Be Thou my Vision, O Lord of my heart;
Naught be all else to me, save that Thou art
Thou my best Thought, by day or by night,
Waking or sleeping, Thy presence my light.

Be Thou my Wisdom, and Thou my true Word;
I ever with Thee and Thou with me, Lord;
Thou my great Father, I Thy true son;
Thou in me dwelling, and I with Thee one.

Be Thou my battle Shield, Sword for the fight;
Be Thou my Dignity, Thou my Delight;
Thou my soul’s Shelter, Thou my high Tower:
Raise Thou me heavenward, O Power of my power.

Riches I heed not, nor man’s empty praise,
Thou mine Inheritance, now and always:
Thou and Thou only, first in my heart,
High King of Heaven, my Treasure Thou art.

High King of Heaven, my victory won,
May I reach Heaven’s joys, O bright Heaven’s Sun!
Heart of my own heart, whatever befall,
Still be my Vision, O Ruler of all.
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Postby Swordguy » Fri Nov 10, 2006 6:11 pm

i would have to agreee with you the calc is fun...once you get the hang of it, make sure you know what is going on though before you move on...though it may take more time it makes things alot easyer
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