Question

lim [(x,y) -> (0,PI/4)] sec(x)tan(y)

when I approach the point along the line y=x, I'm finding that the limit is 0, and that everywhere else the limit is 1. Did I do something wrong? Does this limit not exist?

Answer 1

I dont believe you can use the line y=x as a path, since (0,pi/4) isnt on that path. You have to use paths that go to (0,pi/4). Since (0,pi/4) is defined for the function sec(x)tan(y) and that function is continuous, i would imagine the limit exists.

Answer 2

ah, so as an example, what would be a valid path?

Answer 3

hmm, you could use the path that cuts horizontally through (0,pi/4). So y = pi/4. Or the one that cuts vertically, x = 0. If you want to use a straight line that isnt horizontal or vertical, you can use y = mx+pi/4, and let m be any slope.

Answer 4

alright, so any function, so long as it actually passes through that point (is in the range) would be a valid path?

Answer 5

yes. Thats the most important thing, just making sure the point in question is on that path.

Answer 6

cool cool, thanks!