A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
For which values of c will the limit as x → 5 of the piecewisedefined function f(x) = {ln(x+c) for x>5; sqrt(x4) for x<5 exist?
I have no idea where to start; for the limit to exist at x=5, the function has to approach the same value from both sides, right? But the c is confusing me... please help. Thanks!
 2 years ago
For which values of c will the limit as x → 5 of the piecewisedefined function f(x) = {ln(x+c) for x>5; sqrt(x4) for x<5 exist? I have no idea where to start; for the limit to exist at x=5, the function has to approach the same value from both sides, right? But the c is confusing me... please help. Thanks!

This Question is Closed

Gepard
 2 years ago
Best ResponseYou've already chosen the best response.1for example, if c=5, then there is no limit for ln(x+c), when x>5 try to plot this stuff and you will see, how the "c" affects

freckles
 2 years ago
Best ResponseYou've already chosen the best response.2\[\ln(5+c)=\sqrt{54} \text{ we want left limit equal to right limit} \]

freckles
 2 years ago
Best ResponseYou've already chosen the best response.2\[\ln(5+c)=1 \] You need to solve this

FrozenCthulhu
 2 years ago
Best ResponseYou've already chosen the best response.0I see, that makes sense, thanks... would that mean \[c = e  5\]? That seems ... weird, did I do something wrong? :

FrozenCthulhu
 2 years ago
Best ResponseYou've already chosen the best response.0Oh no, now I closed it but have another question pertaining to this... probably too late :( What would I need to do to find the value of f(5) such that f(x) is continuous at x = 5? It's eluding me :\

freckles
 2 years ago
Best ResponseYou've already chosen the best response.2Well f(5)=lim x> 5 f(x) in order for it to also be continuous at x=5

freckles
 2 years ago
Best ResponseYou've already chosen the best response.2so what did you get for lim x> 5 f(x) ?

FrozenCthulhu
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, it's 1, right? So... f(5) = 1 for f(x) to be continuous at x=5?

FrozenCthulhu
 2 years ago
Best ResponseYou've already chosen the best response.0Ahh, how silly of me, thanks :)
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.