Recent content by Jamie2

thank you! I understand how to finish the problem now. But could you explain your simplification of the left side in a little more detail?

Problem: I plugged in fx, fy, and f(1,pi) everywhere I could but I have no idea how to move on from here. I'm stuck trying to show that: (1+Δx) + (1+Δx)sin(pi+Δy) - 1 = Δx - Δy + ε(Δx,Δy)Δx + ε(Δx,Δy)Δy

along the path y=x x=t y=t limit as t-->0 of sint*sint/t^2+t^2 = sin(0)sin(0)/(0^2+0^2)= 0/0=undefined along the path x=0 x=0 y=t limit as t-->0 sin(t)*sin(0)/t^2+0= sin(0)*sin(0)/0^2+0=0/0 =undefined

I am not sure that this is what the question is asking. Basically I just need help solving the limit definition of derivative algebraically because every time I try I get 0/0= undefined. I need to show the value of the derivative for f(x,y)= xy(x^2-y^2)/(x^2+y^2), at fx(0,0) and at fy(0,0)...

sorry! i made a typo. the original problem has sin(x)sin(y) in the numerator

for both x=0 and y=0 I got that the limit is undefined (0/0)

the problem is that when I try to use the limit definition of the derivative I get that it's undefined (0/0). Do you have any suggestions for how I can compute that limit?

Could you explain in more detail? I don't think I understand what you mean

I got that the limit equals 0 by simplifying the denominator from: ((x2+y2+1)1/2) - 1 to ((x2 - (y+1)(y-1))1/2) - 1 then ((x2 - (y(1+1)(1-1))1/2) - 1 and then evaluating the limit by plugging in 0, getting 0/-1=0 is this correct? is there a better way to do it?

Problem: I did some of the problem on MatLab but I'm having a difficult time evaluating the derivatives at (0,0). Also, MatLab gave me the same answer for fxy and fyx, which according to the problem isn't correct. Any ideas? I used MatLab and computed: fx(x,y)=(2*x^2*y)/(x^2 + y^2) + (y*(x^2 -...

I need help showing that the limit as (x,y)-->(0,0) of (sin(x)sin(x))/x2+y2 does not exist. I've tried approaching the function along the path y=mx, x=y, y=x^3, and several other paths and am not getting any different limits.

on the y axis? is the degenerate surface just a line?

right, I knew that too. But what does that mean for the equation's 3-dimensional surface?

That they are equal to each other? Or that (x-y)2 = -(y-z)2

well that's the same as (x-y)2 + (y-z)2 = 0 but I don't know how to use that to help me describe the quadratic surface