Multivariable Calc Help Needed

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[knotty lichen]

@elfin abyss did you find any points ?

[elfin abyss]

no

[knotty lichen]

(0,0)

It would become 0/0 so undefined there

x=y will not be a point because that's 0/8x²

[elfin abyss]

well, yeah (0,0) is an obvious one

x=y is interesting because the next part of the question asks me to find the limit at each of these points..

[knotty lichen]

Ig its the only one if we don't consider complex numbers

[elfin abyss]

x=y yields infinite possibilites

....

[knotty lichen]

x=y is interesting but it's continuous there

[elfin abyss]

oh

yeah

so only point is (0,0)?

nah can't be that easy lol

[knotty lichen]

It can be

No other real number would give denominator as 0 ?

[elfin abyss]

hmm yeah but

too sus

need an experts opinion on this too verify lol

[knotty lichen]

Lmao ok

[celest laurel]

try partial differentiation?

[elfin abyss]

ye i think ur right

[knotty lichen]

Why tho

[knotty lichen]

Me too

[elfin abyss]

how about for this:

[knotty lichen]

[celest laurel]

idk actually

hmmm

[elfin abyss]

I figured it out

wanna see if u know

[knotty lichen]

Wait lemme try

Oo

[elfin abyss]

go go go

[celest laurel]

(0,0) works

(1,0)

[knotty lichen]

Yee (0,0) is first solution

[celest laurel]

(-1,0)

also work

[knotty lichen]

Yee

[celest laurel]

you get -1/0 in exponent of e

actually

[knotty lichen]

Nah

[celest laurel]

$2x^2 = x^4 + y^2 + 1$

[rotund owl]

Inverse Cupid

[knotty lichen]

Only those 3

[celest laurel]

solutions of that

hmmm

[knotty lichen]

(-1,0),(0,0),(1,0)

[celest laurel]

$x^4 -2x^2 + y^2 + 1=0$

[rotund owl]

Inverse Cupid

[knotty lichen]

[celest laurel]

$x^2 = \frac{2 \pm \sqrt{4 - 4(y^2+1)}}{2}$

[rotund owl]

Inverse Cupid

[celest laurel]

$x^2 = 1 \pm iy$

[rotund owl]

Inverse Cupid

[celest laurel]

so y has to be 0

and then $x = \pm 1$

[rotund owl]

Inverse Cupid

[celest laurel]

alr

@knotty lichen there's only those 3 solutions

(-1,0) ; (0,0) ; (1,0)

[knotty lichen]

Yee

[celest laurel]

I just posted a formal proof of that

[knotty lichen]

Ohh

[elfin abyss]

+close