❖ Lots of Limit Examples, Part 2 ❖

18 Fundamental Limit Examples – Part 2 of 6

In this video, the second part of a 6-part series, we continue exploring a variety of limit questions designed to test and strengthen your understanding of limits.

Remember: All these questions can be solved without L'Hospital's Rule!

In this part, we work through limits involving:

Rational functions
Root functions
Limits at infinity
Difference quotients
And more!

Each problem comes with a detailed solution, ensuring you're fully prepared for first-semester calculus exams. If you’re practicing limits for a comprehensive review, this series is perfect to help solidify your understanding of fundamental limit techniques.

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[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.

[RobertRaleySummers]

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

[deividasmalaska]

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

[jacquesoberholzer]

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

[californiarolllife]

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.

[nicoleybby]

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

[zavayapullo]

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 🧮

[JPbarbosa]

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!

[renewd]

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

[someone]

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.

[Charles-otyf]

Thanks so much for this, calc test tomorrow.

[gradhd]

At 7:26 is that sign analysis?
Thanks

[KarloughPersonal]

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

[kevinli]

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

[sarakalajdzic]

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

[Danny-qurt]

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?

[isaaccruz]

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?

[mim]

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?