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)...
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?
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.