Statement 1: If `f(0)=0,f^(prime)(x)=ln(x+sqrt(1+x^2)),` then `f(x)` is positive for all `x in R_0dot` Statement 2: `f(x)` is increasing for `x >0` and decreasing for `x<0`

Statement 1: Let f(x)=sin(cos x) in [0,(pi)/(2)]* Then f(x) is decreasing in [0,(pi)/(2)] Statement 2:cos x is a decreasing function AA x in[0,(pi)/(2)]

Statement-1: If |f(x)|<=|x| for all x in R then |f(x)| is continuous at 0. Statement-2: If f(x) is continuous then |f(x)| is also continuous.

if f(x)=e^(-(1)/(x^(2))),x>0 and f(x)=0,x<=0 then f(x) is

f(x)=2x-tan^(-1)x-log(x+sqrt(1+x^(2)))(x>0) is increasing in

Let f(x)=cos(x cos((1)/(x))) statement- -1:f(x) is discontinuous at x=0. Statement- 2: Lim -(x rarr0)f(x) does not exist.

Prove that the function f(x)=(log)_(a)x is increasing on (0,oo) if a>1 and decreasing on (0,oo), if 0

If f(x)=(ln(1+x))/x, x in (-1,oo) and f(0)=1 then f(x) is

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)=a(x-x_1)(x-x_2)\ w h e r e\ a ,\ x_1a n d\ x_2\ are real numbers such that a\ !=0\ a n d\ x_1+\ x_2=0. Then which of the following statements is/are always correct? f(x) is increasing in (-oo,0)\ and decreasing in (0,oo) f(x) is decreasing in (-oo,0) and increasing in (0,oo) f(x) is non monotonic on R f(x) has an extremum point

Statement 1: let f(x)=2tan^(-1)((1-x)/(1+x)) on [0,1] then range of f=[0,(pi)/(2)] Statement 2:f decreases from (pi)/(4) to 0