limits

[captian]

:D
hello all
i want the soln of these limits please


lim X^n , 0<X<1 , n tends to infinity
n->infinty

lim X^n , X E R (X belongs to R) , n tends to inifinty
n->inifinty

lim (2^n + 3^n)/(2^n - 3^n) , n tends to infinity
n->inifinity



Thanks alot

[Chad]

I will give these a try :tongue2:

first one

lim ( x^n) n->infinity ( lexus is better :D )

o<x<1

as the power of x goes higher we find that the value goes smaller

e.g : if x= 0.5 , x^2= 0.25 , x^3 = 0.125 ,.... , x^n = 0 where n= infinty

so

lim (x^n) = 0
n->infinity 0<x<1

second one

we have to divide this to three periods

first period : x<-1

if n is odd lim x^n = (-) infinity

if n is even lim x^n = infinity

second period -1 < x < 1 or |x|<1

lim x^n = 0

third period x>1

lim x^n = infinity

third one

I think that we had studied a rule about it in the high school , but I have a crazy solution for it :tongue2:

2^n is always smaller than 3^n

so ( 2^n-3^n ) -> (-) infinity

but on the other side we have ( 2^n +3^n) which tends to infinty

infinity divided on infinty = 0\0