Hello Professor. I'm extremely grateful for your content. It has a level of clarity and friendliness that other instructional videos don't have. Thank you for taking the time to help us, I'm very thankful. Have a wonderful day Professor.
Thank you so much for your kind words, I pour my heart and soul into these videos and am so happy they are helpful to you and students around the world. Wishing you lots of success!!! ☺️☺️☺️
This week I have seen the video from11.1 to 11.4, my goal is finish 11.1-11.10 during these two week. Hope I can do it on time. And thank for your clear explanation!! You always have the best teaching!
Yay great job!!! I have faith that you can get it done if you want to. 👍🏻Thank you for your kind words and all your support, I really appreciate it. ☺️💕
hi, why is it that at 32:45 (n+1)^3 divided by n^3 equals to (1+1/n)^3 ?i thought it would be (1/n^3 + 1/n^2)^3 im just struggling a little bit to understand that part
28:21 oh god limit comparison test proves harder for me… I did limit as n->∞ of (1/2n+3)/(1/n) and got 1/2 as the limit and so 1/2>0 and so I thought because limit is greater than 0, series converges… ugh this is so hard 😭😭😭
😂😂 My students always ask the same thing! For the most part as long as you can compute the limit and the result doesn’t yield an inconclusive test (meaning you get 0 or infinity as your limit) then you should be ok with just Limit Comparison. 👍🏻 Unless your professor specifically asks you to use Direct Comparison in the directions…I get it though, it feels “safer” since you don’t have to worry about showing the correct inequality etc.
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Just wanted to share my appreciation for these videos. They are so well done. Wish my professor in college cared half as much as you. Have a good one.
You are so very welcome, and I really appreciate your feedback! Wishing you lots of success in your studies.
Hello Professor. I'm extremely grateful for your content. It has a level of clarity and friendliness that other instructional videos don't have. Thank you for taking the time to help us, I'm very thankful.
Have a wonderful day Professor.
Thank you so much for your kind words, I pour my heart and soul into these videos and am so happy they are helpful to you and students around the world. Wishing you lots of success!!! ☺️☺️☺️
i honestly love you
This week I have seen the video from11.1 to 11.4, my goal is finish 11.1-11.10 during these two week. Hope I can do it on time. And thank for your clear explanation!! You always have the best teaching!
Yay great job!!! I have faith that you can get it done if you want to. 👍🏻Thank you for your kind words and all your support, I really appreciate it. ☺️💕
If you were my professor i would never skip a class.
😊😊😊 thank you!
hi, why is it that at 32:45 (n+1)^3 divided by n^3 equals to (1+1/n)^3 ?i thought it would be (1/n^3 + 1/n^2)^3 im just struggling a little bit to understand that part
28:21 oh god limit comparison test proves harder for me… I did limit as n->∞ of (1/2n+3)/(1/n) and got 1/2 as the limit and so 1/2>0 and so I thought because limit is greater than 0, series converges… ugh this is so hard 😭😭😭
In the last example, how does (n+1)^3 divided by n^3 equal (1+1/n)^3? I do not understand
Thank you
You're welcome ☺️
Just one question, can we completely ignore the regular comparison test and always do limit comparison test?
😂😂 My students always ask the same thing! For the most part as long as you can compute the limit and the result doesn’t yield an inconclusive test (meaning you get 0 or infinity as your limit) then you should be ok with just Limit Comparison. 👍🏻 Unless your professor specifically asks you to use Direct Comparison in the directions…I get it though, it feels “safer” since you don’t have to worry about showing the correct inequality etc.
I have a question, can I also use the comparison test for example 7?
For exercise 6 25:38. I dont get it why can we do comparison test
love your videos. keep it up 👍 ⬆ 🆙
- from ari
Thank you so much!!!! I appreciate your comment Ari ☺️☺️☺️💕
25:57 not smaller,
greater i guess
Yes I meant to say denominator is larger making the whole expression smaller! 😊
15th comment