- #1
Anne5632
- 23
- 2
- 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 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?
The notation "lim as n tends to infinity" represents the limit of a function as the input variable, n, approaches infinity. This means that we are looking at the behavior of the function as the input value becomes increasingly large.
To compute the limit as n tends to infinity, we need to evaluate the function at larger and larger values of n. This can be done by plugging in increasingly larger values for n and observing the trend in the output values. If the output values approach a specific number as n gets larger, then that number is the limit.
If the limit as n tends to infinity does not exist, it means that the function does not approach a specific number as n gets larger. This could be due to the function oscillating or having a discontinuity as n increases.
Yes, the limit as n tends to infinity can be a negative or complex number. The limit represents the behavior of the function at extremely large input values, and it is possible for the function to approach a negative or complex number as n gets larger.
The limit as n tends to infinity is used in many areas of mathematics, including calculus, analysis, and number theory. It allows us to study the behavior of functions at extremely large input values and can help us understand the long-term trends and patterns in mathematical systems.