6 methods of evaluating the limit of a multivariable function (calculus 3)

6 ways of evaluating the limit of a multivariable function that you need to know for your calculus 3 class! Subscribe to @bprpcalculusbasics for more calculus tutorials!

0:00 1. Just plug in
0:58 2. Do algebra (just like calculus 1)
3:47 3. Substitution
5:23 4. Separable (i.e. the limit of a product is the product of the limits when they both exist)
10:25 5. Polar (when (x,y) approaches (0,0))
15:46 6. Squeeze theorem
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[NixelKnight]

Thanks you so much! I don't have to take Calc 3 at my university, but I've always wanted to learn it. Your videos have been so helpful for me and I really appreciate it!

[IisChas]

I laughed out loud at 15:30 when you drew the frowny face saying that there was no conclusion. I don’t know what it was, but it just got me.

[bprpcalculusbasics]

Be careful when we use the polar method:

[Gabes]

At 18:08 why can’t you just substitute r=0 into the bottom then leave it as (rcos^3@)/cos^2@ then cancel out the cos to get rcos@ then substitute r=0 again to get the limit as 0?

[thepotato]

Can someone explain me why (e^2x - 1)/x is equal to f'(0)? ( I only know math up to derivatives)

[order]

Is there any way to tell whether you should start using the path method to show the limit does not exist or start the Squeeze Theorem?

[joshuahillerup]

Has there been a video showing where the limit of a product exists, but the product of the limits does not exist?

[EmmanuelGiouvanopoulos]

L'Hopital's rule is haunting this man.

[davidcroft]

Is there an equivalent theorem of L'Hopital rule in calc 3?

[aubertducharmont]

My way: set x=y, then use the l'Hopital's rule. It is probably not mathematically correct, but it works, if both x and y are aproaching the same value.

[lday]

Now number 5, the larch.... the larch

[chonkycat]

Why can’t L’Hopital’s rule be used for the substitution method? It’s single-variable?

[SuryaBudimansyah]

Multivarible function is multiterrible