Thread: Determining Points of a Func. That are Continuous

Given the functions below, determine all the points where the function given is continuous.

1.) f(x,y,z) = (x^3)/(y) + sin(z)

2.) Note: this function is a piecewise function:

Code:

f(x,y) = cos(1/(x^2 + y^2)), if (x,y) =! (0,0)
             1,              if (x,y) = (0,0)

Also note that =! means "does not equal"

Any help would be appreciated.

Originally Posted by Ideasman

Given the functions below, determine all the points where the function given is continuous.

1.) f(x,y,z) = (x^3)/(y) + sin(z)

This is some combination of those standard (elementary) functions. Thus, the "bad" points are the undefined points.
In this case it is y=0.

Thus,
S={(x,y,z)| such that y ! = 0}