If `f(x)={x^(2{e^(1/x)},)x != 0 k, x=0` is continuous at `x=0,` where {*} represents fractional part function, then

If f(x)={((sin3x)/(e^(2x)-1),,,x!=0),(k-2,:,x=0):} is Continuous at x=0, then k=

if f(x)=(sin^(-1)x)/(x),x!=0 and f(x)=k,x=0 function continuous at x=0 then k==

If f(x)=(x-e^(x)+cos2x)/(x^(2)) where x!=0 , is continuous at x=0 then (where, {.} and [x] denotes the fractional part and greatest integer)

If f(x)=(x-e^(x)+cos2x)/(x^(2)) where x!=0 , is continuous at x=0 then (where, {.} and [x] denotes the fractional part and greatest integer)

Given f(x)=[log_a (a|[x]+[-x]|)^x((a^((2/(([x]+[-x])))/(|x|)-5))/(3+a^(1/(|x|))) for |x| !=0 ; a lt 1 and 0 for x=0 where [ ] represents the integral part function, then

Number of points on [0,2] where f(x)={(x{x}+1,(0lexlt1),(2-{x},1lexle2):} fails to be continuous or derivable is: (where {.} denotes fractional part function)

The function f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0, at x=0 ,f(x)=0 a. is continuous at x=0 b. is not continuous at x=0 c. is not continuous at x=0, but can be made continuous at x=0 (d) none of these

If int_(0)^(x){t}dt=int_(0)^({x})tdt (where x>0,x!in I and represents fractional part function),then

If domain of f(x) is (-oo,0) , then domain of f(6{x}^2-5(x)+ 1) is (where {.} represents fractional part function)