let `f(x)=(lncosx)/{(1+x^2)^(1/4)-1}` if `x > 0` and `f(x)=(e^(sin4x)-1)/(ln(1+tan2x))` if `x < 0` Is it possible to difine `f(0)` to make the function continuous at `x=0`. If yes what is.the value of `f(0)`, if not then indicate the nature of discontinuity.

Let f(x)=(e^-x)/(1+[x]) , then

Let f(x)=x^(2)(e^(1/x)e^(-1/x))/(e^(1/x)+e^(-1/x)),x!=0 and f(0)=1 then-

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Consider the statements : P : there exists some x in RR such that f(x)+2x=2(1+x^(2)) Q : There exists some x in RR such that 2f(x)+1=2x(1+x) then-

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Which of the following is true?

If f(x) = log_e ((1-x)/(1+x)) , then f' (0) is

Let f(x) (1-cos4x)/(x^(2)),g(x)=(sqrtx)/((sqrt(16+sqrtx))-4)and q(x)=(e^(2x)-x^(x)+1)/(x^(2x+e^(x)+1)),(x in R). lim_(xrarr0)f(x)

If f(x)= (1)/(x+1) - log (1+x), x gt 0 then f(x) is-

Let f(x) (1-cos4x)/(x^(2)),g(x)=(sqrtx)/((sqrt(16+sqrtx))-4)and q(x)=(e^(2x)-x^(x)+1)/(x^(2x+e^(x)+1)),(x in R). lim_(x to 0)g(x)=

If f (x) =log ""(1+x)/(1-x) then-

If f(x) =ln ((x^2 + e)/(x^2 + 1)) , then range of f(x) is