Slant Asymptote Lines: Example 1: Rational Function

1

• 35
• 0
• 0.652

• Published on Nov 19, 2020

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) = x3/(x2+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!

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/slant-asymptote-lines-example-1-rational-function

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
Law of Exponents ax-y = ax/ay: http://youtu.be/djwpuNtmYJY .

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: contact@mes.fm

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

Tags :

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

19:19
2 views 8 months ago \$
10:43
0 views a year ago \$
01:09:22
27 views 8 months ago \$
04:10
1 views a year ago \$
02:14
1 views a year ago \$

More Videos

03:08:08
4 views a year ago \$
03:11
6 views 5 months ago \$
01:19:10
10 views a year ago \$
05:35
14 views 10 months ago \$
40:55
4 views 4 months ago \$
01:29:10
26 views a year ago \$
11:15
3 views a year ago \$
03:12
21 views a year ago \$
01:00:35
13 views a year ago \$
08:54
0 views a year ago \$
20:59
137 views 9 months ago \$
28:45
10 views 9 months ago \$
52:21
23 views a year ago \$
11:51
80 views 9 months ago \$
12:13
1 views a year ago \$
10:29
2 views 7 months ago \$
20:24
4 views a year ago \$
02:38:29
7 views 7 months ago \$
09:10
1 views 6 months ago \$
32:39
7 views a year ago \$
09:31
6 views 3 weeks ago \$
09:55
5 views 9 months ago \$
01:08:21
9 views a year ago \$
14:13
5 views 5 months ago \$
03:59
8 views 7 months ago \$