If `f(x)={(ln x).sgn({x-1/2});1 < x le 3 and {x^2};3 < x le 3.5.` Find the pointswhere the continuity of `f(x),` should be checked, where [.] is greatest integer function and {.} fractional part function.

f(x)={(ln x)*sgn({x-(1)/(2)});1

Discuss the continuity of f(x)=(log|x|)sgn(x^(2)-1),x!=0

If f(x)=ln(1+x)-(tan^(-1)x)/(1+x) , (for x> 0) then sgn f(x) is ( sgn represents signum function)

If f(x)= a^({a^(|x|)sgn x }),g(x)=a^([a^(|x|)sgn x] for a gt 1, a!=1 and x in R , where {**} & [**] denote the fractional part and integral part functions respectively, then which of the following statements holds good for the function h(x) , where (ln a) h(x) = (ln f(x) + ln g(x)) .

If g(x)=ln(1+x)(tan^(-1)x)/(1+x),xgt0 then sgn(g(x)) is,(where sgn(.) represents signum function)

If f(x)=log x and f(1)=0; show then f(x)=x(log x-1)+1

If f(x) = sgn (x) and g (x) = (1-x^2) ,then the number of points of discontinuity of function f (g (x)) is -

If f(x)=int((1-ln(tan^(-1)x))/(1+(ln(tan^(-1)x))^(2)))^(2)(dx)/(1+x^(2)) then f(tan1)-f(tan(1)/(e)) is equal to