❖ Lots of Limit Examples, Part 2 ❖

[@RobertRaleySummers]

"Let's do two more in this video, cause I'm havin funnn!" Hahahaha everyone should strive to be this excited about Math!!!

[@youtubehandlesareridiculous]

Get into math outside of school. It sounds weird, but it is helpful to get interested which is helpful to get better at math, too though.

[@patrickjmt]

+Robert Summers your book is coming! i keep procrastinating; tomorrow I will drop it in the mail (hopefully!)

[@patrickjmt]

+Robert Summers i had two for you, but my wife accidentally returned one as she knew I already had it. She left the good one here though (Bronstein!)

[@RobertRaleySummers]

+patrickJMT no worries!!! Like you said, I'm gonna focus I'm my studies first and chess second. But.... will you please autograph it ;0)

[@patrickjmt]

+Robert Summers ha, sure thing!

[@ungerpharmacy]

Always struggled with limits in high school, even up to calculus, but I never realized how conceptual the process was until you explained limits so well. The diagram at the beginning of part 1 really helped with that.

[@deividasmalaska5793]

people like you deserve all the happiness and good fortune in the world

[@jacquesoberholzer7803]

You are literally singlehandedly pulling me through limits!!! Thank you so Much!!!!!!!!!

[@californiaroll4life]

Thank you this helped me so much! Also for question 4 you can recognize that limit as the formula for the derivative of the function x^-1 and u can differentiate that function at x=2 and you will also get -1/4 in a much faster way.

[@KarloughPersonal]

10:54 dis what my face looks like while studying during this pandemic lmfao

[@zavayapullo2474]

I am so blessed to have found your channel. You explained everything so well. Sir May the math-magician bless you 😊 you’re truly an angel from the calculus paradise 🧮

[@patrickjmt]

ha, what a nice comment :) good luck in your studies and come back any time!

[@nicoleybby]

Thank you!!! I have my first calc exam today on limits and this is such a big help!

[@JPbarbosa8]

The only thing that I can't understand is how a guy like that is not valued properly. You Patrick, give us knowledge more valued than gold. Thanks. E um muito obrigado vindo do Brasil

[@ernestometer]

The second video is really enlightening. I need to really work hard academically in knowing the in-depth of limits.

[@MrMalibujunkies]

Thank you for taking your time and making these,, helped a lot. You are a good person and I really appreciate that! God bless you!

[@someone229]

Limit number 4 can be easily evaluated using the derivative idea. knowing that the basic definition of the derivative within a point (a) is the limit as (h) goes to zero of f(a+h) minus f(a) all divided by (h). Notice that f(a) is always in the top right to the minus sign. So in this case our f(x) is x^-1 and we want to take the derivative of it at x=2 cause we have 2^-1 right to the minus sign which is f(2). The derivative of x^-1 is -1/x^2 and if we plug 2 we get -1/4 which is the answer to our limit.

[@renewd]

Brilliant explanation for number 5 about limits to infinity and negative infinity from left and right (DNE).

[@kevinli4769]

Pre call is hard I finished Saxon advanced mathematics but this really helps

[@nicole115920]

these videos are saving my life rn :D

[@DankPajeet]

Yupp

[@sarakalajdzic389]

so much better at explaining limits in comparison to my professor. thank you.

[@Charles-ot2yf]

Thanks so much for this, calc test tomorrow.

[@someoneunknown5313]

wow, I wish my math notebook was organized that neat and clear

[@unosuryoyo]

More of these please!

[@isaaccruz6261]

On the first question, I don't think you would distribute the minus sign because they were separate fractions. You would simply minus the 2 and be left with h. Right?

[@anantakusumap2459]

Thank you +patrickJMT it was amazing for me

[@JJ14668]

I’m actually feeling so much better about my midterm now 😅

[@hahasel6324]

"squirt of x" im getting too tired. late night cram session xD Whatever, nice video. Really helped me out, thank you good Sir!

[@brenmclean]

For the examples that equal 0/0, I used L'Hopitals rule (ie. Limit of derivatives). Seemed quicker than some of the other ways to find the limit.

[@patrickjmt]

people at the beginning of calculus aren't even doing derivatives yet so how could they use l'hopitals rule?

[@brenmclean]

@@patrickjmt You make a good point. My bad

[@virion5850]

For number 6 you said square root makes a number bigger but isn't the function of a square root .. ultimately going to make a number smaller But still a really helpful video 👍

[@panizr8160]

saved me with these videos!!

[@DankPajeet]

You saved my ass Patrick🤗🤗🤗🤗

[@Danny-qu7rt]

For problem #5, I know we can't use l'hospital's rule in this because we'll get 0(which is a vertical asymptote) but may I ask why? Is there any rules regarding the usage of l'hospital's rule?

[@deepandangal]

function undefined. no use method.

[@raedrid2499]

thanks ,more example will help

[@mim073]

Sir what method did u use for question 7 to turn the whole equation into -3x^5. Do u have a separate video on it, if yes what is the method called?

[@MY-hj1fv]

there is no method to that, it is just the rule that if there is a polynom you only focus on the highest exponent and its constant (in Limits)

[@ioanacoutinho2572]

Thank you 😊

[@Andrea-do4tx]

thanks man! great video. explained very well

[@raizenzoldyck7563]

just wanna ask been watching your video since i was high school did sharpie ever sponsored u? :D

[@pillsburydoughhoe9696]

I'm considering using sharpies and a sketchpad in math class lol! How long do your sharpies last?

[@coBBweBB]

4:56 = Doug Demuro? Is that you?

[@renewd]

Is infinity multiplied by negative infinity actually just a representation of a really large positive number multiplied by really large negative number?

[@orange100pop]

Chris Manhoff Yes

[@stacy-ann1722]

That first question though...omg

[@shaunsmith-milne6257]

Thank you for these videos! Greetings from France :)

[@sammainer8728]

Good teacher

[@rob651]

The 6th and 7th questions have no limit by definition. right?

[@stummstefan9735]

Jokes aside.awsome vid thank you

[@heysiri3327]

On #4, couldn't you also recognize it as a derivative and use the chain rule?

[@zibochen1606]

Helps a lot!

[@marmar2248]

Thanks it’s great

[@azachi260]

God bless you!

[@yugsahu7388]

Number 6 is actually done wrong. The limit of (x^1/2 - x) as you approach infinity is not indeterminate. You should divide both terms by x and you will get (1/x^1/2 - 1). When you plug in infinity as x, x^1/2 will be infinity and any number (in this case 1) divided by infinity is 0. So the answer will be -1.

[@ThatLLMGuy]

Hey can you post a video on examples of Area between the curves.

[@patrickjmt]

+MdZuhair Zuhair i have a lot of those already, search

[@ThatLLMGuy]

thanks

[@eyuafewerk7303]

hi patrick in Q5 when 1/infinitiv you sey that it is infinitive why is the answer is not 0 in my angle of view the ansewr is 0 b/c when 1/infinit number it aprochis to 0

[@IAmNigHtMaReTR]

you are amazing

[@gradhd4359]

At 7:26 is that sign analysis? Thanks

[@sergiolucas38]

very nice video :)

[@hearvie]

Does it mean when you get infinity it does not exist?

[@abcforgt]

Valeu!

[@guimiiranda]

thx

[@Sarah-yl4xf]

Isn't 00×_00 a indefinite form?

[@koyin2270]

God bless you😩

[@sectonsakalani569]

done great thing to me

[@Mak5797]

Hey Patrick can you explain me how you solved quetion number 7 I mean just plugging in the infinity in -3X5 + 4X + 11 = infi - infi + 11 = 11 Please reply. Thank You

[@orengrrrr]

Mudrit As explained in the 6th question infi - infi doesnt equal 0

[@kuznetsov5172]

you cannot sub inf - inf from each other. It may seem like algebra (e.g. a-a=0) but its very different. Infinite numbers are a concept.

[@jannahkhalil9496]

Are postive infinity and infinity the same?

[@SehlaAbdellah]

No Infinity encompasses both +ve and -ve it can be positive or negative but positive infinity is just positive numbers

[@prateekkumawat3533]

I dont get sound in especially your videos. However when I run them in internet explorer i get them. Why is that?

[@nerdon2]

+Prateek Kumawat I'd suggest clearing your cache/cookies.

[@prateekkumawat3533]

+nerdon2 the problem still exists even after clearing cache and cookies. I get this sound problem only on his channel. All other channels work well.

[@patrickjmt]

+Prateek Kumawat i have no idea what is going on...

[@prateekkumawat3533]

patrickJMT thanks for the reply. I think I need to complain google this issue.

[@endamcsweeney5877]

how come on Q.5 you can't use difference of 2 squares for top?

[@purvakantawala9112]

It's (x^2)+1, not (x^2)-1, so it's not a difference of squares.

[@benjaminb.4043]

At which point can you confidently say, that the limit is undefined? In your flowchart you said with (nonzero/zero) it usually is undefined, but how can you prove that a limit is undefined ?

[@patrickjmt]

+Benjamin B. you find the left hand limit and right hand limit and see if they are equal or not. technically, the limit is undefined if it is not any finite number

[@benjaminb.4043]

+patrickJMT Ah thanks for the quick reply! Just a quick question, couldn't you solve 4.) with the rule of l'hopital? Since it is 0/0?

[@patrickjmt]

yes you could, but at the beginning of a calculus class people don't know about derivatives and so don't know about l'hopitals rule yet

[@benjaminb.4043]

Ahh I see, well might be different in other countries, because here in germany the first time you encounter limits is after derivatives. Thanks! Keep up the great work, you are helping a lot of people!

[@basharsy1477]

I cant understand number 4

[@petaiacoka2485]

To all the beautiful people who disliked the video: What is wrong with you!!!?

[@lainelleraine98]

I really don't understand how the infinity thing works 😐😐😐

[@sandragamal8727]

He has a separate video on infinity. Though you probably don't need that anymore, it's been a year

[@isntjinlovely3841]

I don't speak english but im so desperate

[@matiassantacruz5487]

You should ask Khan Academy to add you as an extension. Cause s9me of your videos (a load of them!) beat theirs!!!

[@ElifArslan-l9g]

[@ART69]

Wala ako maintindihan pota xd

[@UltimatePrinceofBB]

Loli Dragon ikaw bubu Jk lang

[@isasakarya7957]

NOT TURKHIS!

[@aishwaryavijayan4375]

your marker making scratchy sound is not cool 😐, you might think it is , but it's not

[@aang7505]

Aishwarya vijayan hb you learn English?

[@edgarsvilums1550]

I agree. It's ruining the experience a little.

[@diy-projects]

turn ur volume off then lol. hes one of the best math youtubers, take what u can get lol. I dont mind the marker