Applying L'Hopital's Rule to Exponential Indeterminate Forms

Поділитися
Вставка
  • Опубліковано 8 лют 2025
  • Description
    0^0, 1^infinity, and infinity^0 are three more indeterminate forms where we have to do further analysis to compute these limits. By taking logs, we can invoke the power of L'Hopital's Rule
    Learning Objectives
    1) Classify a limit as being in an indeterminate form
    2) Apply an appropriate sequence of algebraic tricks to convert it into a "standard" form for L'Hopitals Rule, and compute.
    Now it's your turn:
    1) Summarize the big idea of this video in your own words
    2) Write down anything you are unsure about to think about later
    3) What questions for the future do you have? Where are we going with this content?
    4) Can you come up with your own sample test problem on this material? Solve it!
    Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
    This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.
    BECOME A MEMBER:
    ►Join: / @drtrefor
    MATH BOOKS & MERCH I LOVE:
    ► My Amazon Affiliate Shop: www.amazon.com...

КОМЕНТАРІ • 18

  • @jacksonr260
    @jacksonr260 8 місяців тому +2

    This is the best detailed walk through of this technique I've found. Thanks!

  • @thecosmos7671
    @thecosmos7671 2 роки тому +7

    Watching these series of lectures keeps me on the edge of my seat. I can kind of guess what is coming next and that makes it all the way more exciting. I think this is a great feat you've achieved Professor.

  • @gardenmenuuu
    @gardenmenuuu 4 роки тому +9

    Why are u so underrated us should have at least 1 million subscribers you are a nice combo in 1 video that expresses both what 3 blue 1 brown does and khan academy does in one shot at once(intuitiom and questions)

  • @praveshkumar8267
    @praveshkumar8267 3 роки тому +6

    I am huge fan of your series on calculus especially multivariable one. Can you please do a series on Real analysis as it is a good extension of these concepts. Thank you for your lectures.

  • @certifiedfurryfriend
    @certifiedfurryfriend 4 роки тому +5

    the clear board ur writing on is amazing me wow love that

  • @balakrishnakumar1588
    @balakrishnakumar1588 6 років тому +2

    It's great
    All those lectures

  • @dpmike32819
    @dpmike32819 Рік тому

    What kind of board are you using to work out the problem?

  • @thezoz9476
    @thezoz9476 4 роки тому +1

    Hello, thanks for all these videos
    How do we justify Taking limit of ln(x^sqrt(x))
    then raising it to e being equal?
    My thanks.

    • @DrTrefor
      @DrTrefor  4 роки тому

      Well e^ln(f(x)=f(x), right? And since e^x is a continuous function you can move the limit inside

    • @srghma
      @srghma 2 роки тому

      Or ln(e^f(x))=f(x) 😀

  • @alizaman8407
    @alizaman8407 5 років тому

    Thank u sir

  • @nikitathakur5721
    @nikitathakur5721 7 років тому +1

    it's cool

  • @puremaths2444
    @puremaths2444 3 роки тому +1

    Sir I don't understand the relationship between exponential to logarithmic function

    • @DrTrefor
      @DrTrefor  3 роки тому +2

      They are inverse functions of each other

  • @colewalker2916
    @colewalker2916 3 роки тому +1

    How do you just know that x^-1/2 goes to infinity

    • @Omar-ic3wc
      @Omar-ic3wc 3 роки тому +1

      Hi, x^-1/2 is equal to 1/x^1/2 and if the limits of x approaches 0+ it means that it approaches from the right so x will be very very small number like positive 0.00000000001, 1 divided by a small number like 0.0000000001 will give you a very big number as a result so will definitely lead to infinity.

    • @colewalker2916
      @colewalker2916 3 роки тому +1

      @@Omar-ic3wc oh thank you a lot