# Thread: determine the limits of the following sequences if they exist

1. ## determine the limits of the following sequences if they exist

a) an= cos(n(pi)) b) an= sin^-1( )

c) an= e^(4-n^2)

2. Originally Posted by tiga killa
a) an= cos(n(pi)) b) an= sin^-1( )

c) an= e^(4-n^2)
a)
$cos((2k)pi)=1$
$cos((2k+1)\pi)=-1$
You tell me, could it converge to anything?

b)what is $lim_{n\rightarrow \infty}\frac{2-3n+n^2}{5+2n^2}$?
multiply by $\frac{1/n^2}{1/n^2}$ and see what happens. Hint: you should get 1/2.

Recall: $sin(\pi/6)=1/2$

c)what is what is $lim_{n\rightarrow \infty} 4-n^2$?
Hint: $e^{-x}=\frac{1}{e^x}$