Trisarahtops
  • Trisarahtops
The end behavior of f(x) = 9+2x^3 / x^4-81 most closely matches which of the following? y = 0 y = 2 y = 9 y = −9
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
SolomonZelman
  • SolomonZelman
Evaluate f(10) f(100) f(1000) (use a calculator) and tell me when happens to the function as x grows.
Trisarahtops
  • Trisarahtops
okay gimme a sec
Trisarahtops
  • Trisarahtops
f(10)= .2025

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Trisarahtops
  • Trisarahtops
f(100)= .02000
Trisarahtops
  • Trisarahtops
it gets smaller @SolomonZelman
SolomonZelman
  • SolomonZelman
Yes, and it would continue getting smaller and smaller....
SolomonZelman
  • SolomonZelman
it actually goes to zero...
SolomonZelman
  • SolomonZelman
Do you want to leave with that, or do you want to verify that this is so?
Trisarahtops
  • Trisarahtops
alright so zero is the answer. I've got it thanks ;)
SolomonZelman
  • SolomonZelman
For very large values of x (like x=1000 and bigger) \(\large\color{#000000 }{ \displaystyle 2x^3>9>0 }\) and (also for very large x-values); \(\large\color{#000000 }{ \displaystyle \frac{1}{2}x^4
SolomonZelman
  • SolomonZelman
Do you agree with the last statement? (left side => smaller numerator, bigger denominator right side => bigger numerator, smaller denominator so, left < middle < right)
SolomonZelman
  • SolomonZelman
What will this do? We can simplify both right and left sides and show that they surely go to zero, and therefore the middle (our function would also go to 0.
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle \frac{2x^3}{x^4}<\frac{9+2x^3}{x^4-81} <\frac{2x^3+2x^3}{x^4-\frac{1}{2}x^4} }\) \(\large\color{#000000 }{ \displaystyle \frac{2}{x}<\frac{9+2x^3}{x^4-81} <\frac{24x^3}{\frac{1}{2}x^4} }\) \(\large\color{#000000 }{ \displaystyle \frac{2}{x}<\frac{9+2x^3}{x^4-81} <\frac{48}{x} }\)
SolomonZelman
  • SolomonZelman
and left and right surely go to zero.

Looking for something else?

Not the answer you are looking for? Search for more explanations.