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Define f(x) so that ((x^3)(x^2)x2)/((x^2)4) is continuous at x = 2.
 one year ago
 one year ago
Define f(x) so that ((x^3)(x^2)x2)/((x^2)4) is continuous at x = 2.
 one year ago
 one year ago

This Question is Closed

j814wongBest 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.
 one year ago

zepdrixBest 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
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
dw:1348695490464:dwwoops i missed one of the points :x
 one year ago

zepdrixBest 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?
 one year ago

j814wongBest ResponseYou've already chosen the best response.0
So I'll want to find the left and right limits then?
 one year ago

zepdrixBest 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.
 one year ago

zepdrixBest 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
 one year ago

zepdrixBest 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
 one year ago

j814wongBest 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?
 one year ago

zepdrixBest 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
 one year ago

j814wongBest ResponseYou've already chosen the best response.0
Where did you get the x=/= 2 though?
 one year ago

zepdrixBest 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"
 one year ago

j814wongBest ResponseYou've already chosen the best response.0
Oh ok then. Thanks a lot.
 one year ago
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