What is the Basic Idea of Limits in Calculus?

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In summary, the concept of a limit is the value that a function is approaching but never quite reaching. It can also be thought of as the height a function is trying to reach on the y-axis. In terms of a point (x, y), the limit is (value the function is tending to, limit). This understanding is crucial in mastering calculus, and it is recommended to read the textbook carefully and supplement with video lessons and practice problems to fully grasp the concept.
  • #1
nycmathguy
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Hello everyone. How are you? I want to learn calculus so badly. I plan to do a self-study through calculus l, ll, and lll. Before I think so far ahead, I need a clear, basic definition of the concept of a limit. Textbook language is never easy to grasp unless the student is gifted. I am not gifted mathematically but love the subject.

I understand the limit idea to be the following:

•The value a function is tending to without actually getting there.

•The height a function is trying to reach in terms of the y-axis.

•In terms of a point (x, y), the limit is (value the function is tending to, limit). In other words, x = the value a function is tending to and y = the limit, the height of the function.

Is my understanding of a limit clear or not?
 
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  • #2
nycmathguy said:
•The value a function is tending to without actually getting there.
That's the concept you need. Height and the rest aren't Mathematical.. they're Physics.

-Dan
 
  • #3
topsquark said:
That's the concept you need. Height and the rest aren't Mathematical.. they're Physics.

-Dan

Thank you, Dan. I will post questions showing work as I understand it. Looking for corrections, hints, and a complete solution in some cases.
 
  • #4
Beer induced greetings follow.
nycmathguy said:
Hello everyone. How are you? I want to learn calculus so badly. I plan to do a self-study through calculus l, ll, and lll. Before I think so far ahead, I need a clear, basic definition of the concept of a limit. Textbook language is never easy to grasp unless the student is gifted. I am not gifted mathematically but love the subject.

I understand the limit idea to be the following:

•The value a function is tending to without actually getting there.

•The height a function is trying to reach in terms of the y-axis.

•In terms of a point (x, y), the limit is (value the function is tending to, limit). In other words, x = the value a function is tending to and y = the limit, the height of the function.

Is my understanding of a limit clear or not?
nycmathguy said:
Thank you, Dan. I will post questions showing work as I understand it. Looking for corrections, hints, and a complete solution in some cases.
Welcome back RTCNTC/Harpazo/.../nycmathdad.../mathland...
https://mathforums.com/threads/change-my-username.358139/You kept pestering moderator skipjack back there to change your username and yet you took my advice here to just open a new account. Whatever. I hope you will actually read your book this time around carefully and drop your preposterous"method" of just using the chapter outline.
2. I don't have time to read the textbook lessons. I usually make use of the chapter outline as my guide. For example, Section 1.5 is all about Limits at Infinity. I then search You Tube for Limits at Infinity video lessons. I take notes on everything said in the video lesson. I work out all sample questions with the video instructor. Is this a good way to learn the material?"
And read your book when you're fesh and full of energy; preferably after you've rested and slept (and presumably had some nourishment with coffee shortly afterwards) so that you can maximize your mental energy into understanding and applying what you've been reading and not when "when my brain is tired and I am physically exhausted" as you like to embellish it. Regardless of how passionate you are about math, you can't work/study and concentrate as hard at the end of a study session (in your case, the end of a working day) as at the beginning.

I would also recommend that you subscribe to Jason Gibson's YouTube channel.

https://youtube.com/playlist?list=PLnVYEpTNGNtVp_LDwhDYWE5saOgVQody3
https://youtube.com/playlist?list=PLnVYEpTNGNtVTbp46ZMC-r-jmi_eYHwdQ
https://youtube.com/playlist?list=PLnVYEpTNGNtW6DLLhO0CX8wRWXGymMvny
 
  • #5
I would never say that a function is "trying" to do anything!
 

1. What is the basic concept of limits in calculus?

The basic idea of limits in calculus is the idea of a value that a function approaches as its input approaches a certain point. It is used to describe the behavior of a function near a certain point or as its input approaches infinity or negative infinity.

2. Why are limits important in calculus?

Limits are important in calculus because they allow us to define and analyze important concepts such as continuity, differentiability, and convergence. They also play a crucial role in finding derivatives and integrals of functions.

3. How are limits used in real-life applications?

Limits are used in real-life applications to model and predict various phenomena, such as population growth, economic trends, and physical processes. They are also used in engineering and science to optimize systems and make accurate predictions.

4. What is the difference between one-sided and two-sided limits?

A one-sided limit only considers the behavior of a function as its input approaches a certain point from one direction (either from the left or the right). A two-sided limit considers the behavior of a function as its input approaches a certain point from both the left and the right, and the two-sided limit only exists if the one-sided limits from both directions are equal.

5. Can limits be used to evaluate a function at a point?

No, limits cannot be used to evaluate a function at a point. The value of a limit does not necessarily equal the value of the function at that point, but rather describes the behavior of the function near that point. To evaluate a function at a point, we can simply plug in the value of the point into the function.

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