The limit as n tends to infinity of the function f(xn) is evaluated based on the piecewise definition of f(X), where f(X) = X if X >= 0 and f(X) = X - 1 if X < 0. Given the sequence Xn = -1/n, as n approaches infinity, Xn approaches 0, which is non-negative. Therefore, the limit of f(Xn) as n tends to infinity is f(0) = 0. This confirms that the limit is indeed 0.
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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?