Why do I need to use the squeeze theorem here?

[grim mortar]

In this limit, in my approach, I converted it to polar coordinates and at the end substituted r=0 and got the limit approaching 0 as (x, y) approaches 0.

However, my professor did a similar problem and at the end he used the squeeze theorem instead of substituting r=0.

We both got the same answer, buti s what I did incorrect? Should I have used the squeeze theorem?

[dry cove]

in my opinion your way is fine either

just curious how the -0.5 and 0.5 in Professor's way turn to -(1/2)r and (1/2)r respectively?

[grim mortar]

Oh sorry I forgot to multiply cos(theta)sin(theta) by r

[grim mortar]

Thanks for the help

[night urchin]

@grim mortar has given 1 rep to @dry cove

[dry cove]

urwelcome