Positive integers for k: finding limits

[chapsticks]

Homework Statement

find the positive integers k for which

lim x->0 sin(sin(x))/x^k

Homework Equations

exists, and then find the value of the limit

The Attempt at a Solution

I did the first three k's

k=0
lim x->0 sin(sin x))/x^0= 0 undefined

k=1
lim x->0 sin(sinx))/x^1= 1

k=2 I might be wrong with this
lim x->0 sin(sinx))/x^2= undefined

k>2 how do I do this one.
lim x-> sin(sinx))/x^k>2=?

 

[SammyS]

0 is not positive.

Regarding k = 2: How did you arrive at your answer for k = 1 ??

 

[chapsticks]

well I plugged it into my calculator

 

[flyingpig]

What happens if you multiply and divide sin(x)?

 

[chapsticks]

I'm not sure.

 

[flyingpig]

I'm not sure.

Do it an see what you recognize

 

[chapsticks]

well in the table for k=2

it goes from -100 then an error then 99

so it must be for all positive numbers and above should be infinity?

 

[SammyS]

well I plugged it into my calculator

Are you saying that your calculator says that sin(sin(0))/0 = 1 ?

 

[chapsticks]

I used a different method.. but that answer sin(sin(0))/0 does not exist right

 

[SammyS]

I used a different method.. but that answer sin(sin(0))/0 does not exist right

Right.

So, I ask again. How did you find the answer when k = 1 ?