Limit Question: Calculator Discrepancy

In summary, the calculator states that the limit of the function t(x) is 1 at x = 0, but the graph shows a gap between -1 and 0 and some real values in that section that seem to approach 1. However, based on the given chart, the one-sided limit as x approaches 0 from the positive side is indeed 1, while the limit at x = 0 from the negative side is undefined.
  • #1
Taiki_Kazuma
24
0
Question: Why does my calculator state the limit of the following function is 1, but my calculations state it does not exist?

There's a gap in the graph between -1 and 0. I noticed that there are a few points in that section that do generate real values which appear to move towards 1, but is this enough information to presume the limit is 1 at 0?


t(x) = (1 + [1/x])^x

lim t(x) = ??
x->0


Chart:
x-value____t(x)-value
1_________2.000000
.5________1.732051
.1________1.270982
.01_______1.047233
.001______1.006933
.0001_____1.000921
.000001___1.000014
-.000001___0.999986 - 0.000003i
-.0001_____0.999079 - 0.000314i
-.001______0.993112 - 0.003120i
-.01_______0.954617 - 0.030000i
-.1________0.763453 - 0.248061i
-.5________-i
-1_________undefined
 
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  • #2
What is true is that the one sided limit as x → 0+ is 1.
 

What is a limit question and why is it important?

A limit question is a mathematical problem that asks what value a function approaches as the input approaches a certain value. It is important because it helps us understand the behavior of functions and make predictions about their values.

What is a calculator discrepancy in a limit question?

A calculator discrepancy in a limit question refers to the difference in values obtained when using a calculator to evaluate a limit compared to the actual value of the limit. This can occur due to rounding errors or improper use of the calculator.

How can I avoid calculator discrepancies in limit questions?

To avoid calculator discrepancies, it is important to use the correct input format and precision when entering the limit into the calculator. Additionally, using multiple calculators and comparing the results can help identify and correct any errors.

Can calculator discrepancies affect the accuracy of my results?

Yes, calculator discrepancies can affect the accuracy of your results. It is important to be aware of potential discrepancies and take steps to minimize them in order to obtain more accurate answers to limit questions.

Are there any other factors that can cause discrepancies in limit questions?

Aside from using calculators, other factors that can cause discrepancies in limit questions include human error, incorrect mathematical assumptions, and limitations in the mathematical model being used. It is important to double check all steps and assumptions when solving limit questions to ensure accuracy.

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