- #1

naspek

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## Homework Statement

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)

## Homework Equations

sin x/x = 1

## The Attempt at a Solution

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?