How to find limits on CRAZY GRAPHS (KristaKingMath)

Calculus textbooks like to give you totally funky, disjointed graphs, and ask you to find the limit at various points along the graph.

The purpose of this is to make sure you understand the concept of one-side limits (left- and right-hand limits), and the difference between one-sided limits and general limits. Questions like this also make you show that you know the difference between the value of the function at a particular point and its limit at the same point.

In this video we'll do a limit problem with a crazy graph and examine several points where the function is discontinuous, to find the value of the left- and right-hand limits, the general limit, and the value of the function itself.

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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?!”

[EngineermanCullen]

Absolutely the best explanations I've been introduced to so far. THANK YOU!

[Akinzo]

Thanks a lot! I've been struggling with this for a while now

[chikipichi]

THX YOU. All other videos were covering simple graphs and didn't explain these type of problems

[indian_scouser_ynwa]

krista king, u are the king of calculus.i'm a great fan of your lectures.

[janna]

this is the best tutorial i feel like im gonna cry, thank u so much!! ❤️❤️

[aprilbarrera]

Very helpful and your voice is so soothing.

[charliewatson]

best explanation, I have a calculus quiz tomorrow, this helped me understand limits

[sailbyzantium]

For clarification: if the function DOES NOT specify a number for x (so, just = f(x)), I am looking for a LIMIT. If the function DOES specify a number for x (e.g., f(3)) then I am looking for a VALUE, as in a precise or exact value. Am I understanding that correctly?

So, from your examples, if x --> 3 + (from the right), the LIMIT (empty circle) of f(x) = 1; if x --> 3 - (from the left), the LIMIT (empty circle) of f(x) = 2. In the case of f(x) where x = 3, so f(3), the VALUE (solid circle) is 1.5.

[Moonlight-cepo]

It's our exam tommorow and I'm having a hard time understanding this topic. Thank you for making this video, now I understand the topic in easy and understandble way. Thankyou for saving my life

[daddysaso]

I've been strugling with my Differential Calculus class, but I think I've just found my new teacher!
Thank you so much for the clear and helpful videos! :)

[henaaa]

going to take my basic cal later morning, i pray your teaching helpss TOT

[rajaabbas]

i like your lecture its nice to improve basic knowledge . nice

[BiranchiNarayanNayak]

Excellent tutorial, my concepts are cleared now.

[jennorquiola]

This is exactly what l'm looking for it's very similar to my module thankk u so much

[yeasirarafat]

very well explained, thank you for your effort.

[akifaanzum]

I didn't understand the graphical concepts in the class and many other videos.but now i fully understand the topic clearly.thank you so much❤❤❤💖💖

[ae_strawberry]

This helps me to answer my quiz THANK YOUUUU

[usama]

Can any tell how to plot this function in Mathematica

[sisandatentu]

Wow thanks a lot ... I do understand now ❤️🙏

[akshaysanthosh]

How can one a find value of the function at the discontinuedpooint arithmeticaly (not from graph), obviously we cannot plug the limit, then how?. This is really making me confused