A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Check if the function is continuous.
anonymous
 5 years ago
Check if the function is continuous.

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x) = \left\{ {{{x^2 + 6x  16} \over {x^2 + x 6}}, x \neq 2} \right\}\] \[{7x  4}, x =2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can't order the brackets

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0x^2+x6=(x+3)(x2) x^2+6x16 doesn't have either factor so the limit does not exsit at 3 and 2 so the function is not continuous at either x

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oh x=2 is defined for 7x4

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0still since the limit doesn't exist at x=2 then f is not continuous there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeap. sorry for that.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0all you have to do is make sure the limit exists and the limx>af(x)=f(a) then f is continuous at x=a

nikvist
 5 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\rightarrow 2}f(x)=\lim_{x\rightarrow 2}\frac{x^2+6x16}{x^2+x6}=\lim_{x\rightarrow 2}\frac{(x+8)(x2)}{(x+3)(x2)}=\lim_{x\rightarrow 2}\frac{x+8}{x+3}=2\] \[f(2)=7\cdot 24=10\] \[\lim_{x\rightarrow 2}f(x)\neq f(2)\Rightarrow f(x)\quad not\enspace continuous\]
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.