Let `f(x)=("lim")_(nvecoo){("lim")_(nvecoo)cos^(2m)(n !pix)},` where `x in Rdot` Then prove that `f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l`

Discuss the continuity of f(x)={x^2,xi sr a t ion a l-x^2,xi si r r a t ion a ldot

Discuss the continuity of the following function : f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot

Discuss the continuity of the following function f(x)={1,\ if\ x\ i s\ r a t ion a l , 0\ if\ x\ i s\ irrational

If f(x)=lim_(m rarr oo)lim_(n rarr oo)cos^(2m)n!pi x then the range of f(x) is

Let f(x)=lim_(ntooo) (x)/(x^(2n)+1). Then

Find the value of x where f(x)={x ,\ if\ x\ r a t ion a l1-x ,\ if\ x\ i s\ irrational\ is\ contiuous.

f(x)=lim_(nrarroo)cos^(2n)(pix^(2))+[x] (where, [.] denotes the greatest integer function and n in N ) is

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={0, x in r a t ion a l x ,x in i r r a t ion a l a n dg(x)={O , x in i r r a t ion a l x ,x in r a t ion a l then (f-g)(x)i s (a)one-one and onto (b)neither one-one nor onto (c)one-one but not onto (d)onto but not one-one

The function f(x)=lim_(nrarroo)cos^(2n)(pix)+[x] is (where, [.] denotes the greatest integer function and n in N )