hey,
can't seem to find this limit:
lim((x,y)->(0,0)) ((1+x^2+y^2)^(1/(x^2+y^2+xy^2))
the answer should be "e", but I really don't know how to get there.
appreciate help thanks
use polar coordinates to get
$\displaystyle \displaystyle \lim_{r \to 0}[1+r^2]^{\frac{1}{r^2+r^3\cos(\theta)\sin^2(\theta)}}$
Now rewrite as
$\displaystyle \displaystyle \lim_{r \to 0}exp\left(\frac{1}{r^2+r^3\cos(\theta)\sin^2(\the ta)} \ln\left(1+r^2 \right) \right)$
and use L'hospitials rule on the above.