Let `f(x)=x^(5)[1/(x^(3))],x!=0` & `f(0)=0` (where [.] represent G.I.F.), Then `lim_(xto0)f(x)`

Let f(x)=["sinx"/x], x ne 0 , where [.] denotes the greatest integer function then lim_(xto0)f(x)

Let f(x)={(cos[x],xge0),(|x|+a,xlt0):} (where [.] denotes greatest integer function) If lim_(xto0)f(x) exists then a is:

Let f(x)={(cos[x],xge0),(|x|+a,xlt0):} (where [.] denotes greatest integer function) If lim_(xto0)f(x) exists then a is:

If f(x) ={([x]^2+sin[x])/underset(0)([x])underset("for"[x]=0) "for" [x]ne 0 where [x] denotes the greatest integer function, then , lim_(xto0)f(x) , is

If f(x)=x(-1)^[1/x] xle0 , then the value of lim_(xto0)f(x) is equal to

Let f (x) ={{:((sin pix)/(5x) ",","when " x ne0),(K",", "when" x=0):} If lim _(xto0) lim f(x) =f(0), then the value of K is-

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.

If |f(x)|lex^(2), then prove that lim_(xto0) (f(x))/(x)=0.