A function is definded as
`f(x) = lim_( n to oo) {{:(cos^(2n)x, if xlt 0),(root(n)(1+x^(n)), if 0 le x le 1),((1)/(1+x^(n)),if gt1):}`
which of the following does not hold good ?

A function is defined as f(x)=lim_(x->oo)[cos^(2n) x , if x 1 which of the following does not hold good?

If phi(x)=lim_(n->oo)(x^(2n)(f(x)+g(x)))/(1+x^(2n)) then which of the following is correct

If f (x) = lim _( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of the following is/are true?

Let f(x)=lim_(nto oo) (2x^(2n) sin (1)/(x)+x)/(1+x^(2n)) , then which of the following alternative(s) is/ are correct?

The equivalent definition of the function f(x)=lim_(n to oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)), x gt 0 , is

If f(x)=lim_(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal to

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

Let f(x)=lim_( n to oo)(cosx)/(1+(tan^(-1)x)^(n)) . Then the value of int_(o)^(oo)f(x)dx is equal to

The function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(|x|)-1) .

For each ositive integer n, define a function f _(n) on [0,1] as follows: f _(n((x)={{:(0, if , x =0),(sin ""(pi)/(2n), if , 0 lt x le 1/n),( sin ""(2pi)/(2n) , if , 1/n lt x le 2/n), (sin ""(3pi)/(2pi), if, 2/n lt x le 3/n), (sin "'(npi)/(2pi) , if, (n-1)/(n) lt x le 1):} Then the value of lim _(x to oo)int _(0)^(1) f_(n) (x) dx is: