Grenser og kontinuitet
Lagt inn: 02/02-2006 21:02
Følgende oppgave får jeg ikke til, jeg tror den muligens er litt vrien.
Given a function f(x,y) and a point (a,b) in its domain, define single-variable functions g and h as follows:
g(x) = f(x,b) and h(y) = f(a,y)
If g is continous at x=a and h is continous at y=b, does it follow that f is continous at (a,b)? Conversely, does the continuity of f at (a,b) guarantee the continuity of g at a and the continuity of h at b? Justify your answers.
Given a function f(x,y) and a point (a,b) in its domain, define single-variable functions g and h as follows:
g(x) = f(x,b) and h(y) = f(a,y)
If g is continous at x=a and h is continous at y=b, does it follow that f is continous at (a,b)? Conversely, does the continuity of f at (a,b) guarantee the continuity of g at a and the continuity of h at b? Justify your answers.