It's been a while since I've seen this material, but the notation doesn't look quite right to me. (Perhaps I am just not familiar with it.) From the context of the problem f is a function with multiple independent variables, e.g. f(x,y). Therefore f(x/y) doesn't make sense to me. Is this the same as f(x/y, 0) ?
User Tag List

09082008, 05:01 PM #11My wife and I made a game to teach kids about nutrition. Please try our game and vote for us to win. (Voting period: July 14  August 14)
http://www.revoltingvegetables.com

09082008, 05:59 PM #12
Good LORD! This is why we entj's need the backup of specialists
Mightier than the tread of marching armies is the power of an idea whose time has come

09082008, 08:20 PM #13
Aha! That interpretation works. (Clever, LL)
Note the "d" are actually denoting partials.
f(x,y)=x(x/y,0)
df(x,y)/dx=f(x/y,0)+x[df(x/y,0)/d(x/y)](d(x/y)/dx)=f(x/y,0)+(x/y)[df(x/y,0)/d(x/y)]
df(x,y)/dy=x[df(x/y,0)/d(x/y)](d(x/y)/dy)=(x/y)^2[df(x/y,0)/d(x/y)]
Now note for all x,y:
(df(x,y)/dx)x+(df(x,y)/dx)y=xf(x/y,0)+(x^2/y)[df(x/y,0)/d(x/y)](x^2/y)[df(x/y,0)/d(x/y)]=xf(x/y,0)=f(x,y).
Note that this is exactly the condition we need.
f(x,y)=(df(x,y)/dx)x+(df(x,y)/dx)y
So, the equation for a tangent plane at point (x0, y0, f(x0,y0)) is:
zf(x0,y0)=(df(x,y)/dxx=x0)(xx0)+(df(x,y)/dx)(yy0)
The plane goes throught (0,0,0) if and only if:
0f(x0,y0)=(df(x,y)/dxx=x0)(0x0)+(df(x,y)/dx)(0y0)
Which is the same equation as:
f(x0,y0)=(df(x,y)/dxx=x0)x0+(df(x,y)/dx)y0
And we know the above equation is simply:
f(x,y)=(df(x,y)/dx)x+(df(x,y)/dx)y with (x,y)=(x0,y0)
So all the tangent planes intercept (0,0,0).
Accept the past. Live for the present. Look forward to the future.
Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of [] data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield

09272008, 11:08 PM #14
 Join Date
 Aug 2008
 MBTI
 ENTJ
 Posts
 481

09282008, 10:44 AM #15
Similar Threads

Doing math problem over and over vs flashcards for math
By great_bay in forum Academics and CareersReplies: 10Last Post: 07122017, 08:14 AM 
[ESTP] A problem I can't solve ISTP or ESTP
By ZombieKiller in forum The SP Arthouse (ESFP, ISFP, ESTP, ISTP)Replies: 57Last Post: 07032014, 10:04 AM 
Solve this Math Problem? (With Proof!)
By Ming in forum Academics and CareersReplies: 19Last Post: 05292010, 02:12 PM 
help me figure out this math problem
By Evan in forum The Fluff ZoneReplies: 5Last Post: 07042008, 10:08 PM 
Can somebody please help me with this math problem?
By disregard in forum The BonfireReplies: 5Last Post: 02102008, 04:54 PM