Function continuity and Extreme Value Theorem

[amanda1234]

Hello!

Can somebody please explain how can I show that the function is continuous or not in a given set?

For example [math]f(x,y) = x^2+9/4-y[/math] and the set [math]-2 \le x \le 2 ; -6 \le y \le 6[/math]?

 

[blamocur]

First hint: use parenthesis (unless the function is [imath]x^2 + 2.25 - y[/imath]).

 

[Deleted member 4993]

Hello!

Can somebody please explain how can I show that the function is continuous or not in a given set?

For example [math]f(x,y) = x^2+9/4-y[/math] and the set [math]-2 \le x \le 2 ; -6 \le y \le 6[/math]?

Is it:

f(x,y) =\(\displaystyle \ \frac {x^2 \ + \ 9}{4 \ - \ y}\) .............. that should be written as f(x,y) = (x^2 + 9) / (4 - y)

Those parentheses are super-important. In addition:

Please show us what you have tried and exactly where you are stuck.

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