#Multivariable Calc Differentiation Help Needed
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gleaming basin
I need to determine if z is differentiable at (0,0)
I am finding Z_x(0,0) but am getting a limit which isn't giving me a number which is odd..
where did I go wrong?
any help would be appreciated:
white lynx
since z is a linear combination of functions, it is differentiable at (0,0) iff all the pieces are, so you just want to check whether sqrt(x^2+y^2) is differentiable at (0,0) or not
as that's the only possible place it could go awry
gleaming basin
Is it true that if we have a mutlivariable function and one of the partial derivative DNE, then the function is not differentiable at that point?
white lynx
If it is totally differentiable then the partials exist
If the partials dont exist then it isnt totally differentiable
gleaming basin
Yeah so
Here Z_x(0,0)
the limit does not exist
So it is not differentiable at (0,0) then I guess
white lynx
yep
gleaming basin
hmm my problem is tho...
white lynx
$\lim_{h\to 0}\frac{\sqrt{h^2+0^2}}{h}=\lim_{h\to 0}\frac{\abs{h}}{h}$ which ofc DNE
foggy walrusBOT
Omegabet_
gleaming basin
$\lim_{h\to 0}\frac{\sqrt{h^2+0^2}}{h}=\lim_{h\to 0}\frac{\abs{h}}{h}$ which ofc...
Do u know how I can find this limit above ^ ?
white lynx
Do u know how I can find this limit above ^ ?
go back to calc1 ig?
it's the same as asking whether abs(x) is differentiable at x=0
like I pointed out, all other terms in z are differentiable
so the differenability of z is solely dependent on the differentiability of sqrt(x^2+y^2)
partial wrt x of that piece at the origin DNE
gleaming basin
+close