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

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In summary, as n tends to infinity, the fraction -(1/n) goes to zero, therefore the limit would just be X.
  • #1
Anne5632
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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?
 
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  • #2
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?
Do you want to calculate:$$\lim_{n \rightarrow \infty}f(x_n)$$or$$f(\lim_{n \rightarrow \infty}x_n)$$
 
  • #3
PeroK said:
Do you want to calculate:$$\lim_{n \rightarrow \infty}f(x_n)$$or$$f(\lim_{n \rightarrow \infty}x_n)$$
First one
 
  • #4
Anne5632 said:
First one
Can you write out the sequence ##f(x_n)##?
 
  • #5
-1, -1/2,-1/3,-1/4...
 
  • #6
Anne5632 said:
-1, -1/2,-1/3,-1/4...
That's ##x_n## isn't it?
 
  • #7
What's ##f(x_1)## for example?
 
  • #8
PeroK said:
What's ##f(x_1)## for example?
-1?
 
  • #9
Anne5632 said:
-1?
It's ##-2##, isn't it?
 
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  • #10
Anne5632 said:
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?
 

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

What does "lim as n tends to infinity" mean?

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.

How do you compute the limit as n tends to infinity?

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.

What does it mean if the limit as n tends to infinity does not exist?

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.

Can the limit as n tends to infinity be a negative or complex number?

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.

How is the limit as n tends to infinity used in mathematics?

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.

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