Limits at Infinity

[@MariosMathTutoring]

Want to learn more about limits using PreCalculus Methods? See the video I did here: kzbin.info/www/bejne/pmGTl5-Kfa6hjpo

[@SUHCALVINAMBE]

You're a great tutor, man. I passed my math course with an A because of you.

[@ellastewart8122]

This man deserves all the subscribers in the 🌎

[@strawbkittycake]

I really appreciate and admire your approach to teaching, as well as your comprehensive methods that touch both intuition and logic. Fantastic work, sir!

[@MariosMathTutoring]

Your welcome! I’m glad you like my videos!...thanks so much for letting me know!

[@zeke7515]

As helpful as this was, I don't think I've ever heard anyone say learning limits was exciting. Thanks!

[@MariosMathTutoring]

Your welcome!

[@melanieveliz4210]

I'm glad I came here instead of trying to figure out what the textbook was saying all day. Thank you

[@MariosMathTutoring]

You’re welcome! Glad my video helped you!

[@mothman84]

Where were all these wonderful teachers when I was in high school? :)))

[@theodorz2244]

Love how pedagogical you are when you teach!

[@marsamenace]

thank you mario you are saving my grade

[@badalraj4416]

millions thanks from India too!

[@MariosMathTutoring]

Glad you liked the video Badal!

[@artemikhailov]

IIIII FINALLLYYY UNDERSTAAND

[@RanBlakePiano]

We need you in calculus two !

[@divonnejoaquino325]

Thank you ! This helped a lot, Sir.

[@bittersweeter5882]

Thanks Mr.Mario for the awesome video!

[@gistonenigeria6058]

thank u very much ur video is very good, concise, and straight to the point

[@MariosMathTutoring]

+GISTONE NIGERIA your welcome! Glad you liked and benefitted from the video!

[@daniellal4525]

This is so helpful thank you!

[@danigirl6680]

Very comprehensive, thank you.

[@MariosMathTutoring]

Glad you liked the video!

[@AM-nl5yo]

Omg i can understan 😩 Thank you so much

[@MariosMathTutoring]

Your welcome! Glad my video helped you!

[@sheryalrao4653]

Thank you soo much sir

[@benitoocloo1579]

thanks very useful

[@MariosMathTutoring]

+Benito Ocloo glad you found my video useful.

[@RyanWhitney1]

Well done, thank you

[@MariosMathTutoring]

Your welcome. Glad my video helped you.

[@thiyaga425]

thank you sir

[@MariosMathTutoring]

Most welcome

[@deborahchirambo143]

thank you. ☺

[@MariosMathTutoring]

You're welcome 😊

[@filmsbysteve]

Thank you so much!!!

[@ahmed_deek3590]

I understand this lesson so please learn us differentiation method

[@MariosMathTutoring]

Glad you liked this video Ahmed...I haven’t done any videos yet on differentiation but will keep that in mind for future videos.

[@Muneer398]

Can it be done to process inequalities equation to infinity to form equalities

[@tapsydoodle]

is there a way to do the last one by multiplying 1/highest power?

[@muhammadahsan5169]

Good work

[@MariosMathTutoring]

Thanks! Glad you liked the video!

[@alaamakki9412]

still cant get the third case.... what is the answer supposed to be exactly???

[@fatriantobong2097]

why the answer is not 6 on the third question by dividing everything by x^3

[@ongeziwembhele7579]

Thank you

[@MariosMathTutoring]

Your welcome!

[@dazzlingstar315]

Thank you!

[@MariosMathTutoring]

Your welcome!

[@cads1579]

Thank you!!

[@MariosMathTutoring]

You’re welcome Avi!

[@dhatridongre8849]

Why didn't you solve the 3rd scenario in that rigorous way? By the way, your videos are great and awesome.

[@MariosMathTutoring]

Glad you like my videos! Once you see the reasoning behind the shortcuts you can find the limits quicker in the way I illustrated in the video.

[@frithjof1113]

Thanks sir!

[@MariosMathTutoring]

Your welcome!

[@josevillar5508]

Nice video! But you forgot to write the limits each time you wrote the equals sign

[@AviPars]

The video would be 2 x longer .. I think the students know the point

[@tristanhowse420]

How would I figure it out if the numerator is smaller (3-n^2)/7n^2+4

[@MariosMathTutoring]

You want to look at the highest degree term in the numerator and the denominator...if they are the same degree then it is the ratio of the coefficients...in your example it would be -1/7. Hope that helps!

[@tristanhowse420]

Mario's Math Tutoring sure does thanks!

[@meemee775]

Thz you so much

[@MariosMathTutoring]

+Mee Mee your welcome

[@katrinagarcia8645]

why did you multiply them by 1 / x^2 and I / x ?

[@MariosMathTutoring]

+Katrina Garcia good question...this is just a technique to rewrite the expressions so that is easier to prove or see the limit. Actually if you use the technique of comparing the highest degree term in the numerator with the highest degree term in the denominator you will be able to determine the limit that way...hope that makes sense...this is just a way of 'proving' it.

[@RohitKumar-ky9ee]

Nothing it just made it solved and donot create any change

[@kanwalameen4863]

thanks :)

[@MariosMathTutoring]

+Attia Ameen your welcome!

[@superman123456789210]

would x squared be bigger than 8 squared?

[@MariosMathTutoring]

8 squared is a constant whereas x squared would continue to increase as x approaches infinity ....so yes....as x approaches infinity x squared would be bigger....hope that helps Khanzeh

[@superman123456789210]

Mario's Math Tutoring thanks

[@MariosMathTutoring]

You’re welcome Khanzeh.

[@UnitedStatesFBI]

i love you !

[@charlottekutch5858]

wtf

[@digitalkittycat4274]

Infinity doesn't have any limit ;-)

[@karlchesterinao1209]

pls consider changing your thumbnail its getting kinda steal really good videos though

[@Warriorvenkatofficial]

The light is spoiling your video.

[@RuggedCoyote69]

Thank you

[@MariosMathTutoring]

You’re welcome Rob!