3 variable limit problem.sighs

[iamyes]

Homework Statement

Determine whether the following limit exist. If so, find its value

[sin (x^2 + y^2 + z^2 )] / [(x^2 + y^2 + z^2)^1/2)]
as x,y,z approach 0,0,0

The Attempt at a Solution

i tried to do using the limit of sin Ѳ / Ѳ as Ѳ approaching 0

im from malaysia and this is my assignment question and i can't figure out the way to solve this question

 

[Anonymous217]

I'm not sure if this is right, but here's my attempt:
Let u = x^2 + y^2 + z^2
limit of u approaching 0 of [sin u] / [u^.5]
sin(0) / [0^.5] = 0/0

Therefore, you can use L'hopital's rule.
sin u / u^.5
cos u / .5u^(-.5)
2cos u / (1/u^.5)
2cos u (u^.5)
u = x^2 + y^2 + x^2 = 0 so 2cos(0)(0) = 0.

 

[iamyes]

hey thanks for ur reply!
im not sure if its correct cos i don't know either! =)
but, a million thanks to u for replying!

anyone have some more opinions?
i wud love to discuss more about this =)

 

[HallsofIvy]

Homework Statement

Determine whether the following limit exist. If so, find its value

[sin (x^2 + y^2 + z^2 )] / [(x^2 + y^2 + z^2)^1/2)]
as x,y,z approach 0,0,0

The Attempt at a Solution

i tried to do using the limit of sin Ѳ / Ѳ as Ѳ approaching 0

im from malaysia and this is my assignment question and i can't figure out the way to solve this question

As you say, with $u= x^2+ y^2+ z^2$,
$$\frac{sin(x^2+y^2+ z^2)}{(x^2+ y^2+ z^2)^{1/2}}= \frac{sin(u^2)}{u}$$
Multiply both numerator and denominator by u to write that as
$$u\frac{sin(u^2)}{u^2}$$
and now use $sin(\theta)/\theta$.

 

[iamyes]

As you say, with $u= x^2+ y^2+ z^2$,
$$\frac{sin(x^2+y^2+ z^2)}{(x^2+ y^2+ z^2)^{1/2}}= \frac{sin(u^2)}{u}$$
Multiply both numerator and denominator by u to write that as
$$u\frac{sin(u^2)}{u^2}$$
and now use $sin(\theta)/\theta$.

thanks a lot dat really makes my day both of u gave me the same way of solutions and i think it is the best solution
thanks!