Hi everyone this is my first time here - I'm completely confused not so I thought I may as well ask complete stangers for help!
the question is..
Determine whether the following limit exists. If so, find its value.
lim [sin(x^2+y^2+z^2)] / (x^2+y^2+z^2)^1/2
x,y,z-->(0,0,0)
first, how can i prove that the limit is exist?
i'm thinking of to get the above limit to be something like
[sin (x)]/x = 1
or..
should i use quotient rule..?
hope that someone can guide me solving this question..
ok this is my idea..
if i let t=x^2+y^2+z^2, the limit should be like..
lim (sin t) / (t^1/2)
apply L'Hospital rule,
(cos t) / (t^-1/2) = t^1/2 cos t
am i right?
t=0.. so...
(cos t) / (t^-1/2) = t^1/2 cos t
= 0^1/2 cos 0
= 0
ok.. how am i going to proceed?