The discussion revolves around computing the limit of a function as n approaches infinity, specifically focusing on the function f defined piecewise based on the value of its argument. The sequence in question is defined as Xn = -1/n.
The discussion is active with participants questioning the nature of the limit and the behavior of the function at specific points. Some guidance is provided regarding the sequence and its evaluation, but no consensus has been reached on the limit itself.
Participants are considering the implications of the piecewise definition of the function and how the sequence approaches zero as n increases. There is an emphasis on understanding the relationship between the sequence values and the function's output.
Do you want to calculate:$$\lim_{n \rightarrow \infty}f(x_n)$$or$$f(\lim_{n \rightarrow \infty}x_n)$$Anne5632 said: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?
First onePeroK said:Do you want to calculate:$$\lim_{n \rightarrow \infty}f(x_n)$$or$$f(\lim_{n \rightarrow \infty}x_n)$$
Can you write out the sequence ##f(x_n)##?Anne5632 said:First one
That's ##x_n## isn't it?Anne5632 said:-1, -1/2,-1/3,-1/4...
-1?PeroK said:What's ##f(x_1)## for example?
It's ##-2##, isn't it?Anne5632 said:-1?
If you start with ##n>0##, what would the comparison relation between ##-(1/n)## and ##0## be?Anne5632 said:As n tends to inf, the fraction goes to zero so would the lim just be X?