Does the Limit of (sin[floor(x)])/x Exist as x Approaches 0?

[phymatter]

does lim _x->0 (sin[x])/x exist ? if yes then what is it , iguess 0 , but cannot figure out the reason .. pl. help...
note: [x] is greatest integer less than or equal to x

 

[tiny-tim]

hi phymatter!

does lim _x->0 (sin[x])/x exist ? if yes then what is it , iguess 0

yes

(just choose your delta to be 0.9, whatever your epsilon )

 

[mathman]

If-1 < x < 0, [x] = -1, if 0 < x < 1, [x] = 0. As a result , for x < 0, the limit is -∞ while for x > 0, the limit is 0.

 

[TylerH]

note: [x] is greatest integer less than or equal to x

It's usually called the "floor" function.

I don't think it would exist. lim(x->0+) sin(floor(x))/x = 0 and lim(x->0-) sin(floor(x))/x = ∞. For there to be a limit, lim(x->0+) sin(floor(x))/x and lim(x->0-) sin(floor(x))/x must be equal, they're not.