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+(1)/(x) ) =x^2 +(1)/(x^2) , x ne 0, then f(x) =?

If f(x)=(log)_e((x^2+e)/(x^2+1)) , then the range of f(x)

Compute f'(0^(+)) if f(x)=(x(e^(1/x)-1))/(e^(1/x)+1) :

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

Let f(x)=sin^(-1)((2x)/(1+x^(2))) and g(x)=cos^(-1)((x^(2)-1)/(x^(2)+1)) . Then tha value of f(10)-g(100) is equal to

For x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x) be three given functions. If a function, J(x) satisfies (f_(2) @J@f_(1))(x)=f_(3)(x), " then " J(x) is equal to

Let f(x) = (1 - x)2sin2x + x2 for all x ∈ R, and let g(x) = ∫(2(t - 1)/(t + 1) - ln t)f(t)dt for t ∈ [1, x] for all x ∈ (1, ∞). Consider the statements: P: There exists some x ∈ R, such that f(x) + 2x = 2(1 + x2) Q: There exists some x ∈ R, such that 2f(x) + 1 = 2x(1 + x) (A) both P and Q are true (B) P is true and Q is false (C) P is false and Q is true (D) both P and Q are false.

Let f(x)=sin^(-1)x+|sin^(-1)x|+sin^(-1)|x| The range of f(x) is

If f(x)=log[(1+x)/(1-x)], then prove that f[(2x)/(1+x^2)]=2f(x)dot