L'Hospital's Rule (5 basic examples)
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Күн бұрынLearn how to use L'Hosptial's rule to evaluate limits with the indeterminate forms 0/0 or inf/inf. Subscribe for more calculus 1 tutorials!
0:00 limit of (x^3-2x^2+1)/(x^3-1) as x goes to 0
1:28 limit of (e^x-1-x)/x^2 as x goes to 0
3:03 limit of cos(x)/(1-sin(x)) as x goes to (pi/2)^+
5:48 limit of (cos(mx)-cos(nx))/x^2 as x goes to 0
9:48 limit of (ln(x))^2/x as x goes to in
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@leonardobarrera2816 9 ай бұрын
I love Lopitals rule!! ¡Use the Lopital’s Lu!!!! =) Thanks for this!!!
@rogerkearns8094 9 ай бұрын
Good old Loppy Doll. ;)
@moni40tng 9 ай бұрын
Limit 3: Can you really use LH if the limiit becomes (negative) infinity?
@divisix024 9 ай бұрын
Yes, the limit is allowed to be infinity. You may see this from the proof, for example in the General Proof section in the corresponding Wikipedia page. You would need some preliminary knowledge in calculus like the mean value theorem, though. The key point is that the expression is squeezed between the infimum and supremum of the derivative quotient, while by assumption both the limsup and liminf are just the limit (of the derivative quotient) at that point. When the limsup and liminf take on (negative) infinity, which they are allow to by definition, the desired limit is bounded above by negative infinity or below by positive infinity. This is in a similar vein as the comparison test: if something is always no less than another thing which blows up to infinity at some point, then it must also blow up to infinity at the same point.
@yesMe-K 6 ай бұрын
♥
@makarayann5349 9 ай бұрын
❤😂😂
@thedogatemyhomework8 9 ай бұрын
Great video, but let's never forget you can't do that with sin(x)/x when approaching 0!!! Such a common mistake
@BenDover69831 9 ай бұрын
why?
@thedogatemyhomework8 9 ай бұрын
I will let BPRP from the past explain: kzfaq.info/get/bejne/o8CZg8eqrd-5pnk.html&ab_channel=blackpenredpen
@PsychoPathIodine 9 ай бұрын
@@BenDover69831coz its a formula
@divisix024 9 ай бұрын
@@BenDover69831 because the derivative of sine is derived using that identity, so if you use LH it would be circular
@moni40tng 9 ай бұрын
@@divisix024 If you define sin(x) using power series you don't have that limitation.
@mikefochtman7164 6 ай бұрын
Great video, but I think autocorrect got you. L' HoSpital rule?? I know it's just one letter different, but gave me a little laugh. :)
@SuryaBudimansyah 9 ай бұрын
After seeing this video I think I'll cancel my reservation in the L'Hospital
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