MHB What is the Basic Idea of Limits in Calculus?

[nycmathguy]

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?

 

[topsquark]

•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

 

[nycmathguy]

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.

 

[jonah1]

Beer induced greetings follow.

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?

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

 

[HallsofIvy]

I would never say that a function is "trying" to do anything!