anonymous
  • anonymous
for f(x) = x^2/2, find the largest possible delta such that if 0 < |x+4| < delta, then |(x^2/2) - 8| < 1
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.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I have figured out to factor \[x^{2}\] - 8 to get 1/2 (x-4)(x +4)...I hope that's correct...to make a correlation with delta...
anonymous
  • anonymous
x^2/2 - 8, that is
JamesJ
  • JamesJ
First let's analyze |(x^2/2) - 8| < 1 This is equivalent to | x^2 - 16 | < 2 -2 < x^2 - 16 < 2 14 < x^2 < 18 For x < 0, -sqrt(14) > x > -sqrt(18) 4 - sqrt(18) < x + 4 < 4 - sqrt(14) and this is implied by | x + 4 | < |4 - sqrt(18)| because | 4 - sqrt(18) | < | 4 - sqrt(14) | Hence, given \[ \delta = \sqrt{18} - 4 \] \[ | x + 4 | < \delta \implies \left| \frac{x^2}{2} - 8 \right| < 1 \]

Looking for something else?

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

More answers

anonymous
  • anonymous
thanks!
JamesJ
  • JamesJ
You should draw a graph of y = x^2/2 over the interval |x + 4| < delta and see exactly how this delta works.

Looking for something else?

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