A community for students.
Here's the question you clicked on:
 0 viewing
DHASHNI
 3 years ago
help!!!!!!!!!!!!!!
DHASHNI
 3 years ago
help!!!!!!!!!!!!!!

This Question is Closed

DHASHNI
 3 years ago
Best ResponseYou've already chosen the best response.2if f(x)is continuous at x=0...............find a,b

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6Ok so this means we want the function to have the following properties: \[f(\frac{\pi}{2}) \text{ exist}\] \[\lim_{x \rightarrow \frac{\pi}{2}}f(x) \text{ exist}\] Finally, \[\lim_{x \rightarrow \frac{\pi}{2}}f(x)=f(\frac{\pi}{2})\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6so this means also we need \[\lim_{x \rightarrow \frac{\pi}{2}^+}f(x)=\lim_{x \rightarrow \frac{\pi}{2}^}f(x)\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6so for x=pi/2 f(x)=a we will use this later!

DHASHNI
 3 years ago
Best ResponseYou've already chosen the best response.2myini: the question says that f(x) us continuous at x=0

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6\[f(\frac{\pi}{2})=a\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6oh that's interesting we wouldn't care about a then

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6because that part says x>pi/2

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6i think the question had a typeo

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0Just take a couple of limits using l'hopitals rule. For the first one since \[1\sin^3(\pi/2)=3\cos^2(\pi/2)=0\] the constraints of l'hopital's rule applies for the left limit. Thus, \[\lim_{x\to\pi/2}\frac{1\sin^3x}{3\cos^2x}=\lim \frac{3\sin^2x\cos x}{6\cos x \sin x}= \lim_{x \to \pi/2} 0.5\sin x=0.5=a\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6because there is nothing to do if they aren't talking about pi/2

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0Similarly, solve for b.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6and see imperialist ignored that continuous part at 0 lol

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6but yeah i think they meant at pi/2

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0Yeah, me too, I didn't even notice the zero part.

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0For b, you just do the same thing, except you take the limit as x approaches pi/2 from the right regarding the second half of the piecewise function. Set that equal to 1/2, since you know the limit must be that, and you are done.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6i was trying to make the function continuous everywhere

DHASHNI
 3 years ago
Best ResponseYou've already chosen the best response.2@imper:but the question says that the function is continuous at x=0

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0It's a typo, it's impossible to make it continuous at x=0.

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0You already know how x is defined at zero, that can't be changed, no matter what you make a or b.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6its already continuous at 0

imperialist
 3 years ago
Best ResponseYou've already chosen the best response.0True dat, my bad, I didn't look back at the question and assumed sin was on the bottom.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.6thats why the question makes no sense the work is already done i believe it meant what me and imperialist were trying to do

DHASHNI
 3 years ago
Best ResponseYou've already chosen the best response.2thanks guys !!!!!!!!!!!!!!!!
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.