Show transcribed image text At least one of the answers above is NOT correct. 5×2.25 (1 point) Examine the behavior off(x,y) = as (x, y) approaches (0,0) (a) Changing to polar coordinates, we find lim Sx2.25 lim r-0+ , θ=anything = . Use "theta' for θ. Use "infinity" for . oo" and .-infinity" fok_oo". Use .DNE. for "Does not exist.. (b) Since/(0,0) is undefined, f has a discontinuity at (x,y) = (0,0). Is it possible to define a function g : R2 → R such that g(x,y) =f(x, y) for all (x)) (0,0) and g is continuous everywhere? If so, what would the value of g(0, 0) be? If there is no continuous function g, enter DNE. g(0,0) = | 0 Note: You can earn partial credit on this problem.
At least one of the answers above is NOT correct. 5×2.25 (1 point) Examine the behavior off(x,y) = as (x, y) approaches (0,0) (a) Changing to polar coordinates, we find lim Sx2.25 lim r-0+ , θ=anything = . Use "theta' for θ. Use "infinity" for . oo" and .-infinity" fok_oo". Use .DNE. for "Does not exist.. (b) Since/(0,0) is undefined, f has a discontinuity at (x,y) = (0,0). Is it possible to define a function g : R2 → R such that g(x,y) =f(x, y) for all (x)) (0,0) and g is continuous everywhere? If so, what would the value of g(0, 0) be? If there is no continuous function g, enter DNE. g(0,0) = | 0 Note: You can earn partial credit on this problem.
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