Limits

A Few reasoning and assertion questions -:

f(x) = lim cos(n!2∩x) n is an integer .
n--->∞

g(x) = lim cosn(2∩x)
n--->∞

h(x) = lim {cos(n.x)+2}-n

Range of f = R1 , Domain Of f is D1
Range of g = R2 , Domain Of g is D2
Range of h = R3 , Domain Of h is D3

Which Of the following is not the whole real line ?
1) D1UD2 2) R1cUR3 3) D3 4) R2cUR3

Which is true about R3 ?
1) it has 1 point 2) It has infinitely many points
3) It has 2 points 3) It is an empty set

I guess this is a quesiton from targetiit test series...

as n is an integer, n!(2pix) is a multiple of 2pi. When x is a rational number, n!(2pix) will be an integer for a large value of n. But this will not be true for irrational value of x.
Hence the limit exists for x being rational and the limiting value is given by 1.

g(x) on the other hand will not exist. for any value of x.

h(x) has to be typed properly.. wher does the limit go from?!

Check the thread: http://www.targetiit.com/iit-jee-forum/posts/limits-10322.html

For the first part,

Which Of the following is not the whole real line ?
1) D1UD2 2) R1cUR3 3) D3 4) R2cUR3

One of the answers is 1) D1UD2, as explained in the above thread....

The remaining need, proper defn of h(x)

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