If `f(x) = [x] - [x/4], x in R` where [x] denotes the greatest integer function, then

If f(x) = [x] – [x/4] , x ∈ R, where [x] denotes the greatest integer function, then : (1) lim f(x) (x→4-)exists but lim f(x) (x→4+) does not exist. (2) Both lim f(x) (x→4-) and lim f(x) (x→4+) exist but are not equal. (3) lim f(x) (x→4+) exists but lim f(x) (x→4-) does not exist. (4) f is continuous at x = 4.

If f(x)=([x])/(|x|), x ne 0 , where [.] denotes the greatest integer function, then f'(1) is

If f(x)=([x])/(|x|), x ne 0 , where [.] denotes the greatest integer function, then f'(1) is

If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) is

If f(x)=([x])/(|x|),x ne 0 where [.] denotes the greatest integer function, then f'(1) is

If f(x)=[2x], where [.] denotes the greatest integer function,then

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is