Limits in Calculus: Definition & Meaning. What is a Limit?
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- Опубліковано 20 вер 2024
- In this video, we unravel the concept of limits, providing you with a comprehensive understanding of this fundamental idea in calculus.
A limit is a powerful tool that enables us to analyze the behavior of functions as they approach specific values or infinity. But what exactly is a limit? How does it relate to the intuitive notion of approaching a value? We'll answer these questions and more!
Join us as we break down the definition of a limit step by step, ensuring a clear understanding for both beginners and those seeking a review. We'll explore the formal definition, involving epsilon and delta, and explain its meaning in simple terms. We'll illustrate the concept with real-world examples and visually engaging animations, making the learning process enjoyable and intuitive.
Whether you're a student striving to master calculus or simply someone with a curiosity for mathematical concepts, this video is perfect for you. Don't miss out on enhancing your understanding of limits and unlocking the power of calculus. Hit that play button and let's embark on this enlightening journey together!
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Finally a math teacher that understands the importance of why. The frustration that comes with not understanding why something works has been the sole reason Ive given up on math in the past and now I feel like I’m actually making progress with my understanding!
Same here😢
you really get it. i used to think that I was so dumb but I've realized as I have gotten older that I often get stopped at "why" and when no one ever explains it I just feel like I'm memorizing stuff that is pointless or yeah sure I can figure out the equation but what does any of it mean? i think that there would be a boom in the interest of math and science if the fundamental reason of why was explained
Agreed. Other videos assume you already know ‘why’ and if you don’t you’re dumb
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amazing .easy to understand
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This is the video i was looking for not just jumping into example but first explaining the content ...i really like this ...receive ur flowers sir🌷🌹
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You've given the formal definition and you are explaining all the basics really well. I just can't understand without a defination thanks a lot the definition is crystal clear now 😊😊
amazing, I wish you had your videos in playlist so they play in the correct sequence but the teaching method is amazing, great videos . .thank you
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Very well explained! Great for a beginner or a refresher. 😎 Thank you so much.
The easiest, clearer way a limit can be explained, thanks
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You are Excellent. I hope you are already a professor
I’m home teaching two 7th graders calculus now. I let them wrote a python program to calculate the function of y=(x² -4)/(x-2) within the range of (-10,10), then drew the graph of the function. They observed that there is a crack at x=2 in the graph. And the more numbers they sampled within this range, the more smaller the crack is. The function is getting closer to 4 infinitely and that’s the limit. They got it.
Still, they have difficulty to fully understand the definition. I agree the definition is the rigorous way to define this concept, but why the definition is so chalky? I believe the reason is the mathematicians were challenged with some edge cases which made them to give such a wording of the definition to hedge the concept from being breached. If we could find those edge cases, this definition might look smoother to us.
Outstanding you are teaching method is superb ❤
I have no knowledge of Calculus, yet I totally understood this ! Only question I have is : What Is This Used For ???
instantaneous rate of change
If we notice as we point a hand near a flying feather we see it move away as we get near so in the function of nani level is where we can never touch it that is why first law of thermo dynamics say we can never measure nothing. Then would it be better if we define a threshold is better because we can quantify by a real value of within tolerance then we know reality and not guessing
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Welcome!
Crazy to think most authors of analysis textbooks seem to think that a graph isn’t necessary to explain epsilon and delta
I think, the limit of a function is unique at a given point as we know that the limit doesn't exit if RHL is not equal to LHL.
Eg. lim x->0 1/x
LHL:
lim x->0- 1/x=-infinity
RHL:
lim x->0+ 1/x=+infinity.
Hence limits doesn't exit.
You a real definition of science
Thanku sooo much... Now I clearly understood the concept of limit
Fabulous explanation . Thank you so much sir..
My lecture's explanation does not even come close to yours sir. You are legit
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Epsilon and delta can not only be very-very small, but also can be very-very big)
In real life 3 dimension we face time and space need consideration..
So the point limit , line limit , surface limit , and the volume limit and time had all kind of leak because space is not a flat surface
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Beautiful explanation Sir
Wow! Brilliant explanation
@12:13 did you mean to say approaching a? or x?
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Thank you
Wow you gave limit for limit that stressed us
Well explained
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What is his name
limit
Enough
Please stop repeating
He doesn't know that some of us are here in the morning of our exams😭
He’s trying to to say it many different ways so, everyone gets it.