Need some math help...:-\

[Darien]

Well, I'm reviewing for a midterm, but there are two things that I don't exactly have down. Well, 3, but 2 of these I'm not sure where to begin.

If I'm given a surface, how do I have a tangent plane at some point? One of the examples given is x * y^2 * z^3 = 12 at (3, 2, 1)? Do I just take the gradient and plug in the numbers?

If I'm given something like a sphere (x^2 + y^2 + z^2) = 1, how do I find the equation of the tangent plane parallel to a function (ex here is 2x + y -3z = 2?

Thanks 🙂

Darien

 

[NewSc2]

😕

the only way i got through multivariable calculus was because everybody in there was more confused than i was. i got like a 7/50 on the final and that averaged out to a C. (giving me a B for the class)

-hah sorry that wasn't of much help, but if you go to UCI then maybe the confused people tip was *shrug*

 

[wellerdball]

university of chinese imigrants?is that what they call it?

 

[Darien]

I go to USC.

In my math class, it seems that I'm the only one who's not getting it all...🙁

I hope you're right and it just *seems* that way. Maybe I get it better than most people...:Q

nah...

 

[NewSc2]

Originally posted by: wellerdball
university of chinese imigrants?is that what they call it?

yea... university of civics and integras too. you rarely see any chinese immigrants around.. (thus i did well in my calc class). you mostly see the typical aZn riCeRz around

 

[NewSc2]

Originally posted by: Darien
I go to USC.

In my math class, it seems that I'm the only one who's not getting it all...🙁

I hope you're right and it just *seems* that way. Maybe I get it better than most people...:Q

nah...

heh, good luck on your midterm. we had about a.. 40 person class. and about 6 showed up to lecture, and i doubt more than 30 showed up for quizzes. (if that helps you gauge how well your class is doing)

 

[Darien]

Wow.

Out of his first class of ~50, half show up for lectures, and almost everyone shows up when it's time for a quiz.

 

[NewSc2]

UCI isn't exactly an ivy-caliber school 😱 (but it's a breeze for a few 🙂)

i thought everybody showed up for a quiz too... we would fill up a decent part of the class, and i thought everybody else dropped. Come midterm, every seat was full, and about 5 people had to do their midterm on the floor (myself included)

 

[SaintGRW]

Text

 

[Darien]

Originally posted by: SaintGRW
Text

So I'm stupid because two problems stump me?

Unless you're a math god and are involved in doing things like writing the Putnam exams, I don't want to hear from you.

 

[Darien]

Anyways, I think I got the first one down -- taking a break and then coming back to things helps quite a bit.

given is x * y^2 * z^3 = 12 at (3, 2, 1), I simply set f(x,y,z) = x * y^2 * z^3 = 12.

Take the gradient and evaluate that at (3, 2, 1)...plug in

z - z0 = fx(a,b)(x-a) + fy(a,b)(y-b)

Can someone confirm this?

EDIT: previous way doesn't make much sense...this way makes more sense to me.

 

[SaintGRW]

Originally posted by: Darien

Originally posted by: SaintGRW
Text

So I'm stupid because two problems stump me?

Unless you're a math god and are involved in doing things like writing the Putnam exams, I don't want to hear from you.

just playing around w/ you, i haven't done math in forever, so i don't know how to solve it either, had the pic, wanted to post it, the pics i link to are all just in good fun...no offense by it 🙂 good luck with the math

 

[Darien]

Originally posted by: SaintGRW

Originally posted by: Darien

Originally posted by: SaintGRW
Text

So I'm stupid because two problems stump me?

Unless you're a math god and are involved in doing things like writing the Putnam exams, I don't want to hear from you.

just playing around w/ you, i haven't done math in forever, so i don't know how to solve it either, had the pic, wanted to post it, the pics i link to are all just in good fun...no offense by it 🙂 good luck with the math

Ah, it's cool. Sorry I got bent out of shape for the comment -- I'm just stressed out because of thinking about what problems the professor can put on the exam....

...he seems to LOVE definitions and proofs of theorems...:Q

 

[Darien]

If someone can confirm my work for the second one, that would be great 🙂

Given a sphere x^2 + y^2 + z^2 = 1, find the tanget plane that is parallel to 2x + y - 3z = 2.

f(x,y,z) = x^2 + y^2 + z^2
gradient of f(x,y,z) = <2x, 2y, 2z>

tangent plane is <2, 1, -3>*k = <2x, 2y, 2z>

2x = 2k
2y = k
2z = -3k
x^2 + y^2 + z^2 = 1

x = k; y = .5k; z = -1.5k

substitute in f(x,y,z), and k = (2/7)^.5 or -(2/7)^.5

so there are 2 points which are on a tangent plane that are parallel to 2x + y - 3z = 2.

 

[Darien]

bump

 

[Darien]

bump