Slant Asymptote Lines: Example 2: Horizontal Hyperbola


  • 19
  • 0
  • 0.442
  • Reply

  • Open in the desktop app ADD TO PLAYLIST


    Published on Nov 15, 2020
    About :

    In this video I go over another example on Slant Asymptotes and this time look at the slant asymptote lines of a horizontal hyperbola, which is a hyperbola that extends outwards horizontally. The hyperbola x2/a2 – y2/b2 = 1 where a and b are constants has slant asymptote lines y = +/- (b/a)x. This is proven by applying the definition of slant asymptotes which I covered in my earlier video, and that is the limit as x approaches infinity of the difference between the function and a line approaches zero. In other words the function, in this case the hyperbola, approaches the asymptote lines. In proving this, I first rearrange the hyperbola to write it as y = f(x). But since the function involves square rooting a square, we get a two part function that can be either positive or negative, and thus to save time I combined all of the +/- terms (as well as the limit as x approaches +/- infinity) in just one limit formula. This was a shortcut on my part, but nonetheless the result is the same for this particular example as compared with doing it individually. I will be referencing this example on slant asymptotes for a horizontal hyperbola in my later videos, so make sure you watch this video and understand the derivation!

    Download the notes in my video:!As32ynv0LoaIh5E1eR_74BRIMsvEmA

    View video notes on the Hive blockchain:

    Related Videos:

    Slant Asymptote Lines: Example 1: Rational Function:
    Slant Asymptote Lines + Special Case: Rational Functions and Long Division:
    Hyperbola - Definition and derivation of the equation: x2/a2 - y2/b2 = 1:
    Limits at Infinity: Horizontal Asymptotes: .


    DONATE! ʕ •ᴥ•ʔ

    Like, Subscribe, Favorite, and Comment Below!

    Follow us on:

    Official Website:
    Email me:

    Try our Free Calculators:

    BMI Calculator:
    Grade Calculator:
    Mortgage Calculator:
    Percentage Calculator:

    Try our Free Online Tools:

    iPhone and Android Apps:

    Tags :

    mathematics calculus messcience math science

    Woo! This creator can upvote comments using 3speak's stake today because they are a top performing creator! Leave a quality comment relating to their content and you could receive an upvote worth at least a dollar.

    Their limit for today is $0!
    Time until mes can give away $0 to their commenters.
    0 Days 0 Hours 0 Minutes 0 Seconds

    To comment on this video please connect a HIVE account to your profile: Connect HIVE Account

    More Videos

    0 views a year ago $
    5 views 2 years ago $
    1 views a year ago $
    3 views 2 months ago $
    3 views a year ago $