Left & Right Limits Of A Function (Finding Values Of A Variable)

In summary, the conversation discusses a math problem involving finding the value of "m" in a limit equation. There is confusion about what the question is asking for and how to approach it. Eventually, it is realized that the limit can be evaluated simply by substituting 1 for "x" in the equation. A thank you is given to those who assisted in understanding the problem.
  • #1
CallMeShady
45
1

Homework Statement


11rddt5.jpg



Homework Equations


Only ones I know that are relevant are the equations shown in the question (for the left and right limits).


The Attempt at a Solution


The difficulty that I am having right not is comprehending what is really being asked from the question. From what I understand, then question is asking the "m" values from the left and right limits at the top, and the value for "m" when those limits are the same. However, how would I go about finding the value of "m" if I have no x or y co-ordinates given?
 
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  • #2
CallMeShady said:

Homework Statement


11rddt5.jpg



Homework Equations


Only ones I know that are relevant are the equations shown in the question (for the left and right limits).


The Attempt at a Solution


The difficulty that I am having right not is comprehending what is really being asked from the question. From what I understand, then question is asking the "m" values from the left and right limits at the top, and the value for "m" when those limits are the same. However, how would I go about finding the value of "m" if I have no x or y co-ordinates given?
What is [itex]\displaystyle \lim_{x\to\,1}(8x^3-2m)\ ?[/itex]
 
  • #3
SammyS said:
What is [itex]\displaystyle \lim_{x\to\,1}(8x^3-2m)\ ?[/itex]

That is not given (everything above that I posted is the only thing given). Or are you suggesting that I should calculate that to solve this problem. That expression just defines the limit from the left side. I am unsure on how to calculate that.
 
  • #4
CallMeShady said:
That is not given (everything above that I posted is the only thing given). Or are you suggesting that I should calculate that to solve this problem. That expression just defines the limit from the left side. I am unsure on how to calculate that.
What do you mean, it's not given?

I'm asking you to evaluate the limit, [itex]\displaystyle \lim_{x\to\,1}(8x^3-2m)\,,[/itex] if you can. If you can't, I don't how you can do this problem at all.
 
  • #5
SammyS said:
What do you mean, it's not given?

I'm asking you to evaluate the limit, [itex]\displaystyle \lim_{x\to\,1}(8x^3-2m)\,,[/itex] if you can. If you can't, I don't how you can do this problem at all.


I don't see how I can evaluate that limit... I could isolate "m" though by temporarily assigning "f(x)" as "y". Then I could isolate "m" in terms of "y" => "m(y)".
 
  • #6
Sammy is not asking you to solve for m (i.e., isolate me) - just evaluate the limit, which by the way should be
$$\lim_{x \to -1^{-}}(8x^3 - 2m) $$

Your answer should be in terms of m.
 
  • #7
CallMeShady said:
I don't see how I can evaluate that limit... I could isolate "m" though by temporarily assigning "f(x)" as "y". Then I could isolate "m" in terms of "y" => "m(y)".
[itex]\displaystyle \lim_{x\to\,1}(8x^3-2m) = 8(1)^3-2m=8-2m[/itex]

That's all there is to it !
 
  • #8
I can't believe how easy this question actually was... I was making it too complex due to the fact that I wasn't comprehending this question very well. A sincere thank you to Mark and Sammy for their assistance. I really appreciate it.
 
Last edited:
  • #9
CallMeShady said:
I can't believe how easy this question actually was... I was making it too complex due to the fact that I wasn't comprehending this question very well. A sincere thank you to Mark and Sammy for their assistance. I really appreciate it.

So, what are you results?
 

FAQ: Left & Right Limits Of A Function (Finding Values Of A Variable)

1. What is a left limit of a function?

A left limit of a function is the value that the function approaches as the independent variable (x) approaches a specific value from the left side of the function's graph. It is denoted as f(x-) or limx->c f(x).

2. How do you find the left limit of a function graphically?

To find the left limit of a function graphically, you can approach the specific x-value from the left side of the graph and observe the behavior of the function. The left limit will be the y-value at the point where the graph approaches the x-value from the left.

3. What is a right limit of a function?

A right limit of a function is the value that the function approaches as the independent variable (x) approaches a specific value from the right side of the function's graph. It is denoted as f(x+) or limx->c f(x).

4. How do you find the right limit of a function algebraically?

To find the right limit of a function algebraically, you can substitute the specific x-value into the function and evaluate it. If the function is undefined at that x-value, then you can use limits properties and algebraic techniques to determine the right limit.

5. What is the difference between a left limit and a right limit?

The main difference between a left limit and a right limit is the direction from which the independent variable approaches the specific x-value. A left limit is the value that the function approaches from the left side of the graph, while a right limit is the value that the function approaches from the right side of the graph. In some cases, the left and right limits can have different values, indicating that the function is not continuous at that specific x-value.

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