Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
j814wong
Group Title
Define f(x) so that ((x^3)(x^2)x2)/((x^2)4) is continuous at x = 2.
 2 years ago
 2 years ago
j814wong Group Title
Define f(x) so that ((x^3)(x^2)x2)/((x^2)4) is continuous at x = 2.
 2 years ago
 2 years ago

This Question is Closed

j814wong Group TitleBest ResponseYou've already chosen the best response.0
I know what it means for a function to be continuous at a certain point and I know that the above function is not continuous at x = 2. But I don't understand what the question means when it asks for one to define the function.
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Hmmm i think they're asking you to do something like this.dw:1348695324335:dw we need to find a value for c that will make it a nice smooth curve so whats happening is.. you have a HOLE at x=2, and at x=2. So we want to go in and patch the hole
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
dw:1348695490464:dwwoops i missed one of the points :x
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
so the way to find the y value of the HOLEs is to approach the hole from the left or right :D what operation allows us to get closer and closer and closer to a point, without actually touching it?
 2 years ago

j814wong Group TitleBest ResponseYou've already chosen the best response.0
So I'll want to find the left and right limits then?
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
mm yes i think so :D let me check first, i dont wanna lead you down the wrong path if i made a mistake.
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Hmm ok this problem is a bit nasty, since you need to factor a term out of a cube. I dont really remember how to do that part, i had to enter it into wolfram :( dw:1348696335593:dw lemme rewrite the initial function, cause i think i made a tiny notation error :) so we would have this so far..dw:1348696501525:dw
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
so f(x)=7/4 will plug the hole at x=2 now we need to plug the hole at x=2.. so we'll have to do similar to what we did before, except we need to try and factor an (x+2) from that darn cube D: any of this making sense? XD
 2 years ago

j814wong Group TitleBest ResponseYou've already chosen the best response.0
I got most of it except why did you choose to get a c1 and c2? Or rather,how did you know that x is not equal to 2? In this case, is c defined as the value that plugs in the gap?
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
that's why i corrected the chart, it's not x=c1, its f(x) = c1 , when x=2 the c1 is the Y value that we needed
 2 years ago

j814wong Group TitleBest ResponseYou've already chosen the best response.0
Where did you get the x=/= 2 though?
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
dw:1348697608343:dw lets pretend the graph looks like this see the holes at 2 and 2? those are making our function discontinuous. so to fix that that, we change the function to a piecewise function and we say "no no no, when x=2 or 2, we'll define with a different piece than this function"
 2 years ago

j814wong Group TitleBest ResponseYou've already chosen the best response.0
Oh ok then. Thanks a lot.
 2 years ago
See more questions >>>
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.