Is this function continuous?

lim(x,y)-(-3,3) e^(-xy)(cos(x+y))

Question

Is this function continuous?

lim(x,y)->(-3,3) e^(-xy)(cos(x+y))

anonymous · Answer

$$\lim_{(x,y) \rightarrow (-3,3)} e^{-xy}\cos (x+y)$$

For a better view!

xapproachesinfinity · Answer

well cos is a cont function so is exp function
what the is the problem

xapproachesinfinity · Answer

just evaluating the limit?

anonymous · Answer

Yes! But don't I have to determine continuity before I can plug in the values? If it's not continuous, I have to take the partial derivative, right?

anonymous · Answer

In this case, I'm allowed to just plug it in since it's a continuous function?

xapproachesinfinity · Answer

there is really nothing to determine
cos is a continues function R^2 to R^2
so is exp

xapproachesinfinity · Answer

just evaluate the limit

anonymous · Answer

Thank you!

xapproachesinfinity · Answer

welcome

anonymous · Answer

It's Calc 3!

xapproachesinfinity · Answer

why did you delete the comment lol
i was trying to make sense of it

xapproachesinfinity · Answer

i believe it is continuous i took into account that we are dealing with multivariable calc of course

xapproachesinfinity · Answer

All the standard functions that we know to be continuous are still continuous even if we are plugging in more than one variable now.  We just need to watch out for division by zero, square roots of negative numbers, logarithms of zero or negative numbers, etc.
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see this

thomas5267 · Answer

Both function are differentiable throughout R^2 so it is continuous?

zzr0ck3r · Answer

cos is not a function from R^2 to R^2 @xapproachesinfinity

zzr0ck3r · Answer

differentiable implies continuity yes, but not the other way around (exp |x|)