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1) The function f(x) = 1/(3+x) has domain x ≥ 0 and range 0 < y ≤ 3. 2) The limit of the function x^2 - y^3 as (x,y) approaches (0,0) along different paths is not equal, so the limit does not exist. 3) The function f(x,y) = 2x^2 - y^2 if (x,y) ≠ (0,0) and f(x,y) = 0 if (x,y) = (0,0) is not continuous at (0,0) because the limit does not exist along different paths.

Author

Ameet

Language

EN