Limits at infinity (KristaKingMath)

Learn how to find the limit of a function as x approaches infinity. In other words, if we take x to be infinitely large, what value does the function get close to? To figure this out, you'll need to use algebra to simplify the function, then use L'Hospital's rule several times until the function is simplified enough that you can evaluate it at infinity.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[JustDave]

There is a really cool trick to this just by looking at the powers in both the numerator and the denominator, which I bet you already know but I don’t want to spoil the surprise for anyone. Shortcuts mean nothing if you don’t know "why it works."

Also, great job as always. I’m using your videos to keep my mind sharp for Calc II in the spring. Thank you so much for the explanations.

[kristakingmath]

You could try to multiply both the top and bottom by the numerator, yes. I'm glad you like the videos! No, I didn't get a degree in math, I just tutored it and really like it! :)

[isaaccraig]

This is a good way to get the concept but just for the point of making this easier you should explain that you only need to use the highest degrees and can remove everything else so in this example sqrt(9x^6/x^6)= sqrt(9)=3 provided that you make sure to expand or simplify correctly it works on any function if the highest degree is on the top but not the bottom the answer is infinity, if it is on the bottom but not the top the answer is zero, if the highest degree is on both the it is the ratio.

[kristakingmath]

Dividing everything through by the largest degree term is the shortcut way of doing these problems, yes! :)

[drylandthewanderer]

This one is easier if you divide top and bottom by x^3 rather than using L'Hopital. I was actually looking at this same exact problem this morning. Don't forget to change x^3 to x^6 when you factor it into the radical. It's just limit laws after that.

[kristakingmath]

Love you too! :) Glad you like the videos.

[kristakingmath]

They're usually taught really close to each other, yes! :)

[lsid]

Your're welcome! I thought I would help you, since I get so much help from these videos and besides, you deserves more exposure/views. Thank you.

[kristakingmath]

I'm so glad you like the videos! I'll continue to add more videos about applications of calculus as I can. Thanks, and good luck with your PhD!! :D

[punkyhippo]

I used a different technique and solved this in many less steps and directly got 3 as my answer without any necessary cancellation...

[dylanwade]

Thank you so much!!! Working full time and taking summer classes is not pleasant! I didn't have a book during the first week of class, so this video has absolutely saved me.

[norakau]

I really really benefited from your amazing lesson. I am a non English speaker and i had difficulty to understand from my prof but with your speed pace of teaching is very helpful. Thank you very much.

[Ciukyexacta]

I agree, there was no need to make all the steps that were done in the video. it was enough to bring out the square root of 9 (3), and then prove that all what's left inside the root converges to 1, making the general limit equal 3.

[stephanieng]

wow that was extremely helpful. I learned more in 10 minutes of your video than 30 minutes of sitting in class.

[dostoyevsky]

Thank you very much for the great work. I can honestly say you do a better job at explaining this stuff than my Calculus Professor.

[kristakingmath]

i'm glad the videos are helpful to you. thanks for saying hi! :)

[gouravsharma]

Thankyou so much sister... You have won hearts of many students by your great work.. Am constantly watching your videos they are just wow... It's all your blessings that i am doing this much great in maths... Really thankful sister... Really mesmerized by your voice.. I know that this is an old video but still marking its presence.. You have changed my life.. From a very average to one of the finest.... Truly truly greatful..

[someoneify]

Thank you. I like how you spend your time to answer all the comments!

[crystal_snow]

when this is the actual homework problem you needed help with. <3

[trendingbiz]

You just used the loooong and complicated solutions.