Using Tables to Determine Limits

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In summary, the conversation involved completing a table for the function f(x) = x + 3 as x tends to 2 from the left and right sides. The limit was found to be 5 by evaluating f(x) at values approaching 2 from both sides. A table was also created to show the values and their corresponding outputs. The conversation also included a correction to rearrange the order of the values when approaching 2 from the right side. The conclusion was that the limit of f(x) as x tends to 2 is 5.
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nycmathguy
Homework Statement
Use tables to determine a limit.
Relevant Equations
Linear Equation
:: Tables and Limits

Complete a table for f(x) = x + 3 as x→2 from the right and left.

As x tends to 2 from the left side, the given values for x are: 1.9, 1.99, 1.999.

As x tends to 2 from the right side, the given values for x are: 2.001, 2.01, 2.1.

Let me see if I can do this.

I think this question is just an evaluation exercise. I got to plug all the given x-values to evaluate f(x) as x tends to 2.

Each value of x from the left and right gets closer and closer to 2 but f(x) never reaches 2. By this I mean f(x) gets extremely close to 2 but never becomes 2. Is this not the basic limit idea as taught in first semester calculus?

Moving on. This reply is going to drag. How do you think I feel using my cell phone to type all this work?

Our function f(x) = x + 3 is a line.

As x tends to 2 from the left side, the given values for x are: 1.9, 1.99, 1.999.

f(x) = x + 3

f(1.9) = 1.9 + 3 = 4.9

f(1.99) = 1.99 + 3 = 4.99

f(1.999) = 1.999 + 3 = 4.999

Rounding to the units place, I get 5.
The limit is 5.

Yes?

As x tends to 2 from the right side, the given values for x are: 2.001, 2.01, 2.1.

f(x) = x + 3

f(2.001) = 2.001 + 3 = 5.001

f(2.01) = 2.01 + 3 = 5.01

f(2.1) = 2.1 + 3 = 5.1

Rounding to the units place, I get 5.

I conclude the limit is 5.

All of this tells me that the LHL = RHS = 5.

The limit of f(x) as x-->2 is 5.

You say?

Now to make a table.

For the table as x-->2 from the left side:

x: 1.9... . .1.99...1.999
f(x): 4.9. 4.99. 4.999

For the table as x-->2 from the right side:

x: 2.001...2.01...2.1
f(x): 5.001...5.01...5.1

Trust me, I don't plan to do another "complete a table" problem for a very long time. Is any of this right?
 
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nycmathguy said:
Homework Statement:: Use tables to determine a limit.
Relevant Equations:: Linear Equation

f(2.001) = 2.001 + 3 = 5.001

f(2.01) = 2.01 + 3 = 5.01

f(2.1) = 2.1 + 3 = 5.1

It would be to rearrange inverse order

f(2.1) = 2.1 + 3 = 5.1

f(2.01) = 2.01 + 3 = 5.01

f(2.001) = 2.001 + 3 = 5.001

f(2.0001)= ...
 
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  • #3
anuttarasammyak said:
It would be to rearrange inverse order

f(2.1) = 2.1 + 3 = 5.1

f(2.01) = 2.01 + 3 = 5.01

f(2.001) = 2.001 + 3 = 5.001

f(2.0001)= ...

Thank you for the correction. Everything else is ok. Right?
 

1. What is the purpose of using tables to determine limits?

The purpose of using tables to determine limits is to visually represent the behavior of a function as the input values approach a specific value, known as the limit. This can help in understanding the behavior of a function and making predictions about its values at certain points.

2. How do I read a table for limits?

To read a table for limits, you need to look at the values in the input column and see how they are approaching the given limit value. Then, look at the corresponding values in the output column and see if they are approaching a specific value or if they are oscillating between two values. This can help determine the limit of the function at that specific value.

3. Can I use tables to determine limits for all types of functions?

Yes, tables can be used to determine limits for all types of functions, including polynomial, rational, exponential, logarithmic, and trigonometric functions. However, for more complex functions, it may be easier to use other methods such as algebraic manipulation or graphing.

4. How accurate are the limits determined from tables?

The accuracy of the limits determined from tables depends on the number of data points included in the table. The more data points there are, the more accurate the limit will be. However, it is important to note that the limit is an approximation and may not always be exact.

5. Are there any limitations to using tables to determine limits?

While tables can be a helpful tool in determining limits, they do have some limitations. For example, they may not accurately represent the behavior of a function at a specific point if there are large jumps or discontinuities in the function. Additionally, they may not be able to determine the limit if it approaches infinity or negative infinity.

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