this was our highschool exams lol. where's the epsilon-delta definiton of limits? had a quiz in calc 1 today (which i failed last year) had explaining why a limit f(x) was equal to some real number using epsilon-delta definiton, couldn't think of anything so i just wrote some random stuff lmao
Agreed. Delta-Epsilon definition (and later proofs) is a more rigorous standard. This video was recorded as a review for high school students completing an entry level calc course on an applied engineering and business track. The formal definition was beyond the scope of this general review.
Thanks. That's a good approach after you got the derivative of the numerator. I hadn't worked through the problem ahead of time and anticipated some sine or cosine terms would have canceled. They didn't, and I knew I'd be going over it in class anyway to further clarify to my students.
Complex rational expressions are tricky for some. Not all of my students know when components can move or cancel when there are fractions inside of fractions. I want to make sure everyone knows why we're justified in taking shortcuts sometimes.
Thanks. By the time you got to this, did you already factor out the 2 from the second derivative of the denominator? When recording the video, I simplified the first derivative in terms of sine and cosine as 4(sin(2x)/cos^(2x)) thinking something would cancel. From there, I didn't want to go through the quotient rule in the video knowing that this problem was one I'd need to discuss together with students in class.
@mitchehrman After taking the first derivative I just factored out 2 and was left with 2tan(2x)sec^2(2x) / x Then I just took the second derivative, without simplifying the first one. And then I just substituted 0 in and got 4 as the answer. P.S. sorry for my English, I'm currently living in the uk and still learning it 😅
The temptation to just write "the limit doesn't exist" ...
The color coding is everything, you are definitely professional at this aspect of mathematics 🧐🤓🤜🤙
Wow thank you, you have a good way of explaining these which is both concise yet effective
Glad it was helpful!
I already took Calc 3 and I don’t even remember any of this
😂😂😂
this was our highschool exams lol. where's the epsilon-delta definiton of limits? had a quiz in calc 1 today (which i failed last year) had explaining why a limit f(x) was equal to some real number using epsilon-delta definiton, couldn't think of anything so i just wrote some random stuff lmao
Agreed. Delta-Epsilon definition (and later proofs) is a more rigorous standard. This video was recorded as a review for high school students completing an entry level calc course on an applied engineering and business track. The formal definition was beyond the scope of this general review.
Thanks man this helps a lot
Great video! Thanks!
boutta fail my final
me tomorrow
Me in about 3 weeks.
@@cocainejeezusHow do you fail 3 weeks in advance 💀
☠️
@@cocainejeezusthen study💀
You didn't have time for e)? It takes like 1 minute? It's just the product rule on 4sec^2(2x)tan(2x) to get 16tan^2(2x)sec^2(2x) + 8sec^4(2x)
Thanks. That's a good approach after you got the derivative of the numerator. I hadn't worked through the problem ahead of time and anticipated some sine or cosine terms would have canceled. They didn't, and I knew I'd be going over it in class anyway to further clarify to my students.
I was with you until you actually wrote the division symbol at 14:10. What? No one uses that past elementary school. Just move the 2x to the bottom.
Complex rational expressions are tricky for some. Not all of my students know when components can move or cancel when there are fractions inside of fractions. I want to make sure everyone knows why we're justified in taking shortcuts sometimes.
The solution for question e is:
lim
x->0 ( 2tan(2x)(-sin(x)/cos^3(x)) + 4sec^2(x)sec^2(x)) = 4
Thanks. By the time you got to this, did you already factor out the 2 from the second derivative of the denominator? When recording the video, I simplified the first derivative in terms of sine and cosine as 4(sin(2x)/cos^(2x)) thinking something would cancel. From there, I didn't want to go through the quotient rule in the video knowing that this problem was one I'd need to discuss together with students in class.
@mitchehrman After taking the first derivative I just factored out 2 and was left with 2tan(2x)sec^2(2x) / x
Then I just took the second derivative, without simplifying the first one. And then I just substituted 0 in and got 4 as the answer.
P.S. sorry for my English, I'm currently living in the uk and still learning it 😅
in chile we study this topics at school lol
this is a school course lol.
Come to india
in india we did this in 4th grade
are you actually serious????
in (insert country) we did that in kindergarten
Thanks
*L'Hopital (not L'Hospital, ha)
Agreed. I've seen it spelled both ways, but I suspect L'Hopital is *more* correct.
I don’t even have calc why am I here
Because Calculus is awesome.
@@mitchehrman I’m scared 💔
Its very simple no way some students can get under 100%