- #1
mathnerd15
- 109
- 0
Apostol Limit Problem?
I can't afford the Apostol calculus vol. 2 there's a printing mistake in my copy of Apostol and I'm not sure how to prove this, p.251
let f(x,y)={xsin(1/y) if y doesn't equal 0
and f=0 if y=0
prove that the iterated limits are not equal and that the f(x,y)->0 as (x,y)->(0,0)
how exactly do you prove the limit for (x,y)->0 from all possible paths, parabolic paths, x=y, polar paths?
Homework Statement
I can't afford the Apostol calculus vol. 2 there's a printing mistake in my copy of Apostol and I'm not sure how to prove this, p.251
let f(x,y)={xsin(1/y) if y doesn't equal 0
and f=0 if y=0
prove that the iterated limits are not equal and that the f(x,y)->0 as (x,y)->(0,0)
Homework Equations
The Attempt at a Solution
how exactly do you prove the limit for (x,y)->0 from all possible paths, parabolic paths, x=y, polar paths?
Last edited: