Slant Asymptote Lines: Example 1: Rational Function
In this video I go over a quick example on Slant Asymptote Lines and this time look again at the special case, which is a rational function in which the numerator has a degree just one higher than the denominator. The example I cover is determining the slant asymptote line of the function f(x) = x^3/(x^2+1). Since it is a rational function, i.e. a division of two polynomials, and with the numerator a degree of 3, which is one more than the numerator’s degree of 2, we can simply use polynomial long division because as illustrated in my earlier video, the quotient is the asymptote line, and in this case is y = x. Nonetheless, I prove that the quotient is in fact the linear asymptote by applying the definition of a slanted asymptote, which is the limit as x approaches infinite of the difference between f(x) and its linear or slanted asymptote must approach zero, which it in fact does in this case. Graphing the two functions, we can clearly see that f(x) approaches y = x on both the positive and negative infinity scales. This is a very good video into illustrating how to solve for slanted asymptotes for rational functions, so make sure to watch this video!
Video notes and playlist:
- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh5AbeYu6JJH5X3qtLw
- HIVE notes: https://peakd.com/mathematics/@mes/slant-asymptote-lines-example-1-rational-function
- Slant Asymptotes playlist: https://www.youtube.com/playlist?list=PLA196AE9726C3DC6A
Related Videos:
Slant Asymptote Lines + Special Case: Rational Functions and Long Division: https://youtu.be/QX2nfi5JtQs
Euclidean Division of Polynomials: Theorem and Proof: https://youtu.be/ONxn17okl5c
Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y
Rational and Algebraic Functions - A Brief Explanation: http://youtu.be/4mvNTeXEW-k
Slant Asymptotes - Guidelines to Curve Sketching: http://youtu.be/1pk9ZPPyXGo
Rational and Algebraic Functions - A Brief Explanation: http://youtu.be/4mvNTeXEW-k
Law of Exponents a^(x-y) = (a^x)/(a^y): http://youtu.be/djwpuNtmYJY .
------------------------------------------------------
Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
-
28:26
Math Easy Solutions
3 months ago $0.04 earnedSlant Asymptote Lines + Special Case: Rational Functions and Long Division
2321 -
13:43
Math Easy Solutions
4 months ago $0.03 earnedSlant Asymptote Lines: Example 2: Horizontal Hyperbola
1781 -
9:32
The Solution Manual
2 months agoRational Expressions Explained #algebra #rationalexpression
53 -
13:44
Akalucherie
2 months agoAlgebra Essentials: Key Terms Every Student Should Know
20 -
10:17
The Solution Manual
2 months agoFOILing, Multiplying, and Adding/Subtracting Polynomials with Examples
363 -
16:16
The Solution Manual
2 months agoRadicals and Rational Exponents w/ Examples #precalculus #algebra #mathematics
57 -
1:45
DrOfEng
2 months agoDetermine Limits using Algebraic Manipulation - AP Calculus AB/BC
2 -
15:29
InDiscovery
1 month ago $0.04 earnedHints on Quadratic Function and it's graph.
40 -
11:58
The Solution Manual
1 month agoPolynomial Practice Problems #algebra #mathematics
24 -
1:36
DrOfEng
2 months agoDetermine Limits using their Algebraic Properties - AP Calculus AB/BC
3