Answer:
lim (x, y, z) → (0, 0, 0) [x*y*z]/(x^2+y^2+z^2)=0
Step-by-step explanation:
First, we need to put the spherical coordinates equations that we will use in our problem
x = p*sin∅cos Ф
y = p*sin∅sinФ
z=p*cos∅
Then we will state the problem
lim (x, y, z) → (0, 0, 0) [x*y*z]/(x^2+y^2+z^2)
Using the spherical coordinates we get
(x^2+y^2+z^2) = p^2
Which will make our limit be
lim p→0+ [p*sin∅cos Ф*p*sin∅sinФ
*p*cos∅]/(x^2+y^2+z^2)
after solving limit:
lim (x, y, z) → (0, 0, 0) [x*y*z]/(x^2+y^2+z^2)=0
