I wrote down what my teacher said but I still don't understand. Evaluating limits! Reddit r/calculus
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- Опубликовано: 3 окт 2024
- Learn how to evaluate this limit! This is a rather tricky and confusing limit since we have to consider the limit as x comes from the left-hand side and also the right-hand side. Both limits exist but are they equal? This exponential case is tricky! This limit is from Reddit r/calculus.
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Original post on Reddit: / wo4khjonsk
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But if we Use L'Hospital's Rule we get answer in 1 step, 3+2 = 5
Instead of long division, you can +3 then -3 in the numerator. +2 + 3 gives 5. Factor the 5 out, and numerator and denominator will cancel leaving 5.
bro thats such a nice idea
Oh I didn't fully pay attention since I thought that was what he did because it's such a standard trick
Adding 0 is just as important as multiplying by 1. Very useful to know how to do.
You can also +5 and -5!
Out of curiosity, how do you come up with this neat trick? Is this years of experience of playing with numbers or is there a trick?
I don't even have math in school anymore, but these videos are just so relaxing and enjoyable.
I am an Indian. I always eagerly wait for your new video. You are an excellent teacher. I am also a mathematics teacher, but you are my teacher. I am grateful to you.
It is my humble request to you that please explain the concept of hyperbolic trigonometric function in detail.
Thanks for telling your an Indian, that's the most important info
@@alien3200Yes That will be a lot of help in your plan of colonisation
@@vaibhavgupta8681 brother i am an Indian too 😂😂
Aami bangali
I'm a german math teacher. Haven't tought any limits besides the bare minimum for derivatives in 20 years.....
For such questions based on exponential function,One of the most short and elegant method is to study the graph of e^x as when we move towards positive x axis the graph increases rapidly but when we move negative x axis at -∞, we get the value of e^-∞ as zero.
It might be complex but whn u know it u feel another level of satisfaction 😊😊😊;)
First substituting y = x-4 (then limes y -> 0) helps simplifying.
You could have seperate the sum into two limits. One with exp fraction and the other is 2. For the first one divide by the exponential term. At the end you will get 3 + 2=5
There's more to it, because you have to do it from left and right, but I absolutely agree about just adding 2 to the result!
For the positive limit, I don't know if using rates of growth is allowed, but since terms are summed, only the exponent term matters in the fraction as it grows to infinity. You ignore the +1 and cancel out the exponent terms, giving you a result of 3 for the entire fraction. For the negative limit, exponents evaluate to 0, so you get 0 for the entire fraction.
Why should one combine the two fractions? That is not necessary at all and only complicated the calculation.
For x going to -4 from the left, you can immediately use that the exponential factor goes to zero, and hence you get 3*0/(0+1) + 2 = 2.
For x going to -4 from the right, the exponential factor goes to infinity, and hence you have an infinity / infinity situation. But that can be remedied by multiplying the numerator and denominator of the first fraction with e^(-1/(x+4)) and simplifying. Since e^(-1/(x+4)) goes to zero when x goes to -4 from the right, you then immediately get 3/(1+0) + 2 = 5.
Combining factors was part of the question BPRP was responding to.
Sidestepping that and just presenting a quick and easy solution to the problem isn't very helpful if the person wants help understanding their teacher's working out.
@@Silvar55x The original question was simply to compute the limit. The solution which the teacher gave involved combining fractions, yes. But bprp could have shown how to do it quicker and easier _additional_ to explaining the teacher's solution.
@@bjornfeuerbacher5514Sorry, by "original question" I meant the question / plea for help that BPRP was responding to. Should have been more clear.
@@Silvar55x I meant that, too. It's clear that bprp is answering that. My point was that bprp should _additionally_ have pointed out how to do it easier and quicker.
How am i gonna understand math without this guy bro❤ thanks bro we love you and your videos
Thank you, too! Best wishes.
Another great video. I think you could have saved a little work if you did the long division on the first term right at the start. That would give you a 3 with a -3 remainder. The 3 then would combine with the 2 to give you 5
I guess that means if you were to graph the function there would be a discontinuity at x=-4.
I'm not a math student and i have started watching your videos😮 i find it very interesting
Keep up the hard work bro❤
true
Thank you, I will
The Wolfram Alpha plot of this is educational in this context
I am on the lunch break but your video still got me doing maths
Man you're good!! Do you do physics videos too?
I don't understand can't u just do e^(1/x+4)=e^((x+4)^-1) and since e^n^m=e^(n*m) that equals to e^(-x-4) and when u do the limit that equals to 1
I think it's the parentheses. You're doing e^((x+4)^-1) not (e^(x+4))^-1.
To say it another way, e^(1/(x+4)) is not 1/(e^(x+4))
Am I the only one why learnt about polynomial long division just now?
I only heard of it once and didn't really understand it so yes lol.
I'm curious about when it's applicable
Yes
I was, finally, brave enough to watch your video, this one, about limits and e!
Well, I didn't know it was about that before I started watching, so, I was brave enough to continue watching after realizing...
You make so not-scary! Thank you!
Me: 3.5 ± 1.5
High School and Undergrad math majors look away, this answer is just for Undergrad Physics Gang:
On the last black line before it turns blue at 2:27, you can just say "(5 * Big Thing + 2) = (5 * Big Thing)" and "(Big Thing + 1) = (Big Thing)", then cancel out big thing to get 5
That's not even physics
That's the fundamental theorem of engineering
Polynomical divisions are sick 💫💫💫
very clear, even i understood
I fully understand his answer.....but I would not have been able to do this from scratch on my own
That's why practice is important, unless you are used to doing questions like this and activating your brain in such a way, starting it off is very difficult.
It's like understanding a foreign language movie through subtitles, and practicing the actual dialogue itself.
if graph can be presented for completely solution it would be nicely, as well.
The fact that neither 2 nor 5 is one of the choices makes this question too easy!
if you substitute e^(1/x+4) with u, x->(-4)- become u->0, and x->(-4)+ become u->+inf. That would be way faster
You wrote that wrong. You are missing required grouping symbols: e^[1/(x + 4)] is the correct form.
Excellent
Great video
All the six y/os be like when they see the word 5ex: 🤨
Can’t you just use LH-rule.
Its not neccessary to use L'Hôpital's rule here and since the original post was tagged with "pre-calculus" its better to do a more analytical approach
Easyyyy
0:23: 📚 Explanation of evaluating limits with common denominators and combining fractions.
3:45: 📝 Understanding how to evaluate limits using polynomial long division with an example calculation.
7:37: 📈 Understanding the evaluation of limits using exponential functions with positive and negative infinity.
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