How can one prove that a function is continuous?

Asked Mar 30 '21 at 09:56

Active Mar 30 '21 at 10:00

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I have the given function, $$ f(x,y)=1+\sin^2(xy)+\cos(x+y) $$ I am wondering how can I prove that it is continuous on its domain? The limit of this function is 2 as x,y approach zero. However I am not sure how to use the limit to prove continuity on the domain D_f.

Any help appreciated!

edited Mar 30 '21 at 10:00

asked Mar 30 '21 at 09:56

4

sums, products, compositions of continuous functions are continuous. – peek-a-boo Mar 30 '21 at 09:59
Corrected f. Thanks for answers so far – Mar 30 '21 at 10:01
What is your definition of $\sin$ and $\cos$? – Mar 30 '21 at 10:01
continuous and differentiable everywhere along x axis – Mar 30 '21 at 10:02
@MattiP. Corrected function – Mar 30 '21 at 10:06

How can one prove that a function is continuous?

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