TargetIIT

Q1 Find  F(x)=lim[ss]n→∞[/ss]([frac]x[p]2n[/p]f(x)+g(x)[/]x[p]2n[/p]+1[/frac])
when:
a)x<-1
b)-1<x<0
c)0<x<1
d)x>1
where f(x) and g(x) are continuous functions

Q2 lim[ss]n→∞[/ss]  [frac]a[p]n[/p][/]n![/frac] ; a ε R

Q3 lim[ss]n→∞[/ss] (1+[frac]1[/]a[ss]1[/ss][/frac])(1+[frac]1[/]a[ss]2[/ss][/frac])(1+[frac]1[/]a[ss]3[/ss][/frac])...(1+[frac]1[/]a[ss]n[/ss][/frac])
where a[ss]1[/ss]=1 and a[ss]n[/ss]=n(1+a[ss]n-1[/ss]) for n≥2

ans 1)

a)   lim= f(x)               x<-1
b)  lim = g(x)              -1<x<0
c)  lim=g(x)                0<x<1    
d   lim = f(x)                   x>1

2) 0

http://targetiit.com/iit-jee-forum/posts/limits-11996.html

How ?

do you have the answers ? tell whether they are correct or wrong.

@anirudh hoe did u do
2nd one ?

[im]http://codecogs.izyba.com/gif.latex?a%5E%7Bn%7D%3De%5E%7Bn*lna%7D[/im]

thus
[im]http://codecogs.izyba.com/gif.latex?%5Cfrac%7Ba%5E%7Bn%7D%7D%7Bn%21%7D%3D%20%5Cfrac%7B1+%5Cfrac%7Bn*lna%7D%7B1%21%7D+%5Cfrac%7B%28n*lna%29%5E%7B2%7D%7D%7B2%21%7D+...%7D%7Bn%21%7D[/im]

above limit n→0 is zero.

3) 1
is it correct?

@rajat ans for 3rd is e ......its a very common q [im]http://www.mathlinks.ro/images/smiles/wink.gif[/im].....i posted teh link for it btw..