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Multivariable Calculus HELP!

A photo of jreid00 jreid00
i am self studying and i have a question. hope someone knows the answer!

if the directional derivative Df_(3/5, 4/5) (1,2) = 7 and Df_u (1,2) <= 7 for every unit vector u. what is Df_(-5,15) (1,2)?
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@jreid00 wrote
i am self studying and i have a question. hope someone knows the answer!

if the directional derivative Df_(3/5, 4/5) (1,2) = 7 and Df_u (1,2) <= 7 for every unit vector u. what is Df_(-5,15) (1,2)?



Most people on this forum are high schoolers or just finished first year, if you want help with math try asking on http://www.physicsforums.com/
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A photo of BrownianMotion BrownianMotion

@jreid00 wrote
i am self studying



Nerd.

Anyways, you are in luck. You have my brilliance at your disposal.

What the question implies is that (3/5, 4/5) is the unit vector that maximizes the directional derivative of the function at the point (1,2). So it has to point in the same direction as the gradient. Additionally, the magnitude of the gradient is the rate of change of the function in this direction. So,



Therefore,



I may be hungover, but I am positive this is how to solve the problem posed.
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A photo of jreid00 jreid00
yes 63 is the correct answer. i just didn't know how to get it. thanks!

i have another question. :p

let D be the region inside the circle r = 2*cos theta and above the line y=x.

1) express the area of D as an iterated integral in polar coordinates.
2) evaluate the integral.
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First multiply by r to get x^2 + y^2 = r^2 = 2r cos theta = 2x. In other words, (x - 1)^2 + y^2 = 1 which represents a circle centered at (1,0) with radius 1. The line y=x crosses the circle at (0,0) and (1,1). So the area is











Who's yo daddeh?
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A photo of jreid00 jreid00
im not sure how u went from step 3 to 4...
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A photo of BrownianMotion BrownianMotion
There's a trigonometric identity that says cos 2x = 2cos^2 (x) - 1. Rearranging, you have 2cos^2 (x) = cos 2x + 1.
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A photo of jreid00 jreid00
thx!!! i could kiss you! :p
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For some reason I thought you were a dude.
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A photo of jreid00 jreid00
i am. ;)
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A photo of BrownianMotion BrownianMotion
You have a mancrush on me. It's understandable. It's perfectly natural (even for heterosexual males - just as mynameismattgomlgo.) Just don't flood my PM with your lustful desires.

However, I will say that if I was gay, I would be the best gay lover out of all the gay people in the entire world. It's really a shame that gay people like yourself cannot experience what many broads have already experienced, and what many many many many more will experience in the future.

On a related note, this thread has taken a strange turn.
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A photo of jreid00 jreid00

@BrownianMotion wrote

However, I will say that if I was gay, I would be the best gay lover out of all the gay people in the entire world. It's really a shame that gay people like yourself cannot experience what many broads have already experienced, and what many many many many more will experience in the future.



haha whats that? erectile dysfunction? :p
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@BrownianMotion wrote
You have a mancrush on me. It's understandable. It's perfectly natural (even for heterosexual males - just as mynameismattgomlgo.) Just don't flood my PM with your lustful desires.

However, I will say that if I was gay, I would be the best gay lover out of all the gay people in the entire world. It's really a shame that gay people like yourself cannot experience what many broads have already experienced, and what many many many many more will experience in the future.

On a related note, this thread has taken a strange turn.



I want to be more like you
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I would advise against that. ;)
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