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!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5AbeYu6JJH5X3qtLw
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/slant-asymptote-lines-example-1-rational-function
Related Videos:
Slant Asymptote Lines + Special Case: Rational Functions and Long Division:
Euclidean Division of Polynomials: Theorem and Proof:
Polynomial Long Division - In depth Look on why it works!:
Rational and Algebraic Functions - A Brief Explanation:
Slant Asymptotes - Guidelines to Curve Sketching:
Rational and Algebraic Functions - A Brief Explanation:
Law of Exponents a^(x-y) = (a^x)/(a^y): .
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
Google Plus: https://mes.fm/gplus
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]
Try our 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
Try our Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
▶️ DTube
▶️ IPFS
I don’t always determine the slant asymptote line of a rational function but when I do I usually know the final answer before completing the full polynomial long division step ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/slant-asymptote-lines-example-1-rational-function