Let `f(x)={1/(|x|)for|x|geq1a x^2+bfor|x|<1iff(x)` is continuous and differentiable at any point, then `a=1/2,b=-3/2` (b) `a=-1/2,b=3/2` `a=1, b=-1` (d) none of these

Let f(x)=|x|+|x-1|, then

Let f(x)= {{:((x)/(1+|x|)",", |x| ge1), ((x)/(1-|x|)",", |x| lt 1):}, then domain of f'(x) is:

Let f(x)=|x-1| . Then,

Let f(x)={0 for x=0 x^2 sin (pi/x) for -1 1 or x <-1

Let f(x)={(tan^(-1)x, , |x|ge1),((x^(2)-1)/4, , |x|lt1):} then domain of f'(x) is

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

Let f(x)={((x-1)^2 sin(1/(x-1))-|x|,; x != 1), (-1,; x=1):} then which one of the following is true?

Let f(x)={(|x+1|)/(tan^(- 1)(x+1)), x!=-1 ,1, x!=-1 Then f(x) is

Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :} then f(x) is derivable at x =1 , if

Let f(x)=x-1/2 log (x^(2)+1) . Then f' (x) is :