- #1

- 655

- 2

find all points that are continuous in the function f

f(x,y) = (y-5)cos(1/x2) if x not = 0

if x = 0, then f(x,y) = 0

3. The Attempt at a Solution

my notes says that to show continuity, i must show that f(x,y) = f(a,b) when x,y tends to a,b

how do i do that?

does it mean i do something like this

-1< cos(1/x2) <1

-(y-5) < (y-5)cos( 1/x2) < (y-5)

so all points are continuous from -(y-5) to (y-5) except at x = 0 ?

so for f(x,y) = 0 when x = 0, it is not continuous right? since cos(1/0) = undefined?

so all points are continuous from -(y-5) to (y-5) except at x = 0 ?

thanks!