A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
for f(x) = x^2/2, find the largest possible delta such that if 0 < x+4 < delta, then (x^2/2)  8 < 1
anonymous
 4 years ago
for f(x) = x^2/2, find the largest possible delta such that if 0 < x+4 < delta, then (x^2/2)  8 < 1

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I have figured out to factor \[x^{2}\]  8 to get 1/2 (x4)(x +4)...I hope that's correct...to make a correlation with delta...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.2First 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 \[ \delta = \sqrt{18}  4 \] \[  x + 4  < \delta \implies \left \frac{x^2}{2}  8 \right < 1 \]

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.2You should draw a graph of y = x^2/2 over the interval x + 4 < delta and see exactly how this delta works.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.