one good way to tackle xy limits is to convert to polar coordinates, then let r->0
f(r,theta) = r^2/(sqrt(r^2+64)-8)
now, using lHospital's Rule,
lim = 2r/[2r/(2sqrt(r^2+64))]
= 2sqrt(r^2+64))
= 2*8 = 16
Since the function does not involve theta, the limit is the same from all directions.
Find the limit, if it exists. (If an answer does not exist, enter DNE.)
lim (x, y)→(0, 0)
of (x^2 + y^2)/[((x^2 + y^2 +64)^.5)-8]
2 answers
but there is no lHospitals rule in multivariable