f(x,y)=(2x^2+y^2)e^-x^2-y^2 examine the behivour of f when x^2+y^2 large

Question

experimentx · Answer

exponential  function are always greater than power of something ...

blockcolder · Answer

$$f(x,y)=(2x^2+y^2)e^{-(x^2+y^2)}$$
So as x^2+y^2 gets large, 2x^2+y^2 gets large but e^-(x^2+y^2) gets small. It becomes an indeterminate form of sorts.

experimentx · Answer

check this out http://www.wolframalpha.com/input/?i=lim+x-%3Einf+x^100000*1.0001^%28-x%29

blockcolder · Answer

But this is 2 variables. :P

anonymous · Answer

so I got the answer but yhis might be my exam question i just write this I dont need to any calculation ?

experimentx · Answer

but exponential function grows faster than quadratic or paraboloid part ..

experimentx · Answer

http://www.wolframalpha.com/input/?i=plot+%282x^2%2By^2%29e^%28-x^2-y^2%29

asnaseer · Answer

experimentX is right, the limit of this function is zero because the exponential part pulls the function down faster than the other terms.