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# let f(x)=(3x 2 +2x+14)/(1-5x 2 ). The horizontal asymptote is given by y=?

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let f(x)=(3x2+2x+14)/(1-5x2). The horizontal asymptote is given by y=?

round to 1 decimal place

Deathstroke_rule  Feb 26, 2017

#8
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let f(x)=(3x2+2x+14)/(1-5x2). The horizontal asymptote is given by y=?

round to 1 decimal place

$$f(x)=\frac{3x^2+2x+14}{1-5x^2}\\ \text{The horizontal asymptotes is }\\ f(x)=\displaystyle\lim_{x\rightarrow \pm \infty}\frac{3x^2+2x+14}{1-5x^2}\\ f(x)=\;-\;\displaystyle\lim_{x\rightarrow \pm \infty}\frac{3x^2+2x+14}{5x^2-1}\\ \text{Now the numerator and the denominator tend to infinity}\\ \text{so use l'Hopital's theorum}\\ f(x)=\;-\;\displaystyle\lim_{x\rightarrow \pm \infty}\frac{6x+2}{10x}\\ f(x)=\;-\;\displaystyle\lim_{x\rightarrow \pm \infty}(\frac{6}{10}+\frac{2}{10x})\\ f(x)=\;-0.6$$

You can also do this using algebraic division.  It is almost as easy. :)

Melody  Feb 27, 2017
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#1
+86600
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The hrizontal asymptote occurs at  3 / -5    =  -3 / 5   =  -0.6

Here's a graph : https://www.desmos.com/calculator/8mj0jllvgy

CPhill  Feb 26, 2017
#3
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There is not much explanation here Chris

Melody  Feb 27, 2017
#4
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Hey......gimme' a break.....I was answering questions for 4 straight hours....!!!!...I can't give "expanded" explanations to every single one....!!!!!

CPhill  Feb 27, 2017
#5
+92458
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ok ok keep your hat on!     :D

Here, take a break and drink this.  I will make you feel better :)

Melody  Feb 27, 2017
#6
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LOL!!!.....it looks good....but.......you don't happen to have something a bit "stronger,' do you???

I think I'm gonna' need it......

CPhill  Feb 27, 2017
#7
+92458
+5

Mmm ok, here is some Turkish coffee,

It should be strong enough!

Melody  Feb 27, 2017
#8
+92458
+5

let f(x)=(3x2+2x+14)/(1-5x2). The horizontal asymptote is given by y=?

round to 1 decimal place

$$f(x)=\frac{3x^2+2x+14}{1-5x^2}\\ \text{The horizontal asymptotes is }\\ f(x)=\displaystyle\lim_{x\rightarrow \pm \infty}\frac{3x^2+2x+14}{1-5x^2}\\ f(x)=\;-\;\displaystyle\lim_{x\rightarrow \pm \infty}\frac{3x^2+2x+14}{5x^2-1}\\ \text{Now the numerator and the denominator tend to infinity}\\ \text{so use l'Hopital's theorum}\\ f(x)=\;-\;\displaystyle\lim_{x\rightarrow \pm \infty}\frac{6x+2}{10x}\\ f(x)=\;-\;\displaystyle\lim_{x\rightarrow \pm \infty}(\frac{6}{10}+\frac{2}{10x})\\ f(x)=\;-0.6$$

You can also do this using algebraic division.  It is almost as easy. :)

Melody  Feb 27, 2017
#9
+1508
0

You guys are hilarious!

MysticalJaycat  Feb 27, 2017