Compute lim as n tends to infinity of f(xn)

[Anne5632]

Homework Statement

Compute the lim of f(xn)

Relevant Equations

Let f(X) =X if X>=0
And f(X)= x-1 if X<0
Let Xn = -1/n

As n tends to inf, the fraction goes to zero so would the lim just be X?

 

[PeroK]

Homework Statement:: Compute the lim of f(xn)
Relevant Equations:: Let f(X) =X if X>=0
And f(X)= x-1 if X<0
Let Xn = -1/n

As n tends to inf, the fraction goes to zero so would the lim just be X?

Do you want to calculate:$$\lim_{n \rightarrow \infty}f(x_n)$$or$$f(\lim_{n \rightarrow \infty}x_n)$$

 

[Anne5632]

Do you want to calculate:$$\lim_{n \rightarrow \infty}f(x_n)$$or$$f(\lim_{n \rightarrow \infty}x_n)$$

First one

 

[PeroK]

First one

Can you write out the sequence $f(x_n)$?

 

[Anne5632]

-1, -1/2,-1/3,-1/4...

 

[PeroK]

-1, -1/2,-1/3,-1/4...

That's $x_n$ isn't it?

 

[PeroK]

What's $f(x_1)$ for example?

 

[Anne5632]

What's $f(x_1)$ for example?

-1?

 

[PeroK]

-1?

It's $-2$, isn't it?

 

[plum356]

As n tends to inf, the fraction goes to zero so would the lim just be X?

If you start with $n>0$, what would the comparison relation between $-(1/n)$ and $0$ be?