A community for students.
Here's the question you clicked on:
 0 viewing
mathcalculus
 one year ago
HELP: CONTINUITY B=?
(attached below)
mathcalculus
 one year ago
HELP: CONTINUITY B=? (attached below)

This Question is Closed

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.0plug in x = 3. You'll get a number for the first function and set the second function equal to that value. Plug in 3 for x and solve for b.

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.0in the second function

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i did i got it wrong.. :/

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0can you show me how you would do it?

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.0From the first equation:\[4(3)6=126=6\] Thus 7(x)+b = 6 when x=3. So \[7(3)+b=6 \rightarrow 12+b=6 \rightarrow b=21+6=27\] Is this what you got?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0yes, i missed one step, thank you.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0I got it, thanks alot.

surjithayer
 one year ago
Best ResponseYou've already chosen the best response.0Please note a function is continuos at x=a, if (1) L.H.L=R.H.L (2) \[\lim_{x \rightarrow a} f(x)=f(a)\] \[\lim_{x \rightarrow 3}f \left( x \right)=\lim_{x \rightarrow3}\left( 4x6 \right)\] \[put x=3h,h>0,h \rightarrow 0 as x \rightarrow 3\] \[\lim_{x \rightarrow 3}f \left( x \right)=\lim_{h \rightarrow 0}\left\{ 4\left( 3h \right)6 \right\}=4\left( 30 \right)6=6 \] \[\lim_{x \rightarrow 3+}f \left( x \right)=\lim_{x \rightarrow 3+} \left( 7x+b \right)\] \[put x=3+h,h \rightarrow 0,as x \rightarrow 3+\] \[\lim_{x \rightarrow 3+} f \left( x \right)=\lim_{h \rightarrow 0} \left\{ 7\left( 3+h \right)+b \right\}\]=7(3+0)+b=21+b Because f(x) is continuous at all real values \[Hence \lim_{x \rightarrow3}f(x)=\lim_{x \rightarrow 3+} f(x)\] 6=21+b b=6+21=27
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.