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 2 years ago
Use numerical and graphical evidence to conjecture value(s) for the limits, if they exist. If not, describe what is happening at x = a graphically.
 2 years ago
Use numerical and graphical evidence to conjecture value(s) for the limits, if they exist. If not, describe what is happening at x = a graphically.

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onegirl
 2 years ago
Best ResponseYou've already chosen the best response.01) lim x> 1 (x^2  1)/(x + 2) 2) lim x> 1 (x^2 + 1)/(x  1)

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0@UnkleRhaukus umm can u help?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.11) \[\lim\limits_ {x\to1}\frac{ x^2  1}{x + 2}\] what happens when we put x=1 into the fraction

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1yeah, do you know what that simplifies to ?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0okay so how would i describe it?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1can you fill in the table dw:1359329822568:dw

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so for the 2 one i'm dividing 5 to 0 so will it be 5/0 since i cant divide that?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0ok so i got dw:1359330562610:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359330502446:dw

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0how about now? dw:1359331215777:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1(sorry my internet cut out for a moment there) um you got most of them right the first time but check the case when x=1 agian dw:1359331049113:dw

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so then i draw the graph? right ?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1yeah not plot those points dw:1359331297137:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359331448238:dw maybe i should have chosen some better x points

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0what are the question marks and the lines?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1ive put question marks for for the x=2, y=5/0 bit

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359331760380:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1if i chose better x values we would have got something like this

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so that will be the end of the problem?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359332271558:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359332425565:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359332578040:dw

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0ok so this is the final graph?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1this shape is called a hyperbola at x=2 y is undefined, this is because if we look at the graph is should be +∞ and also ∞ but it can't be more than one point we call this a vertical Asymptote

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1359332784659:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1to describe what is happening at x=a if \(a < 2\) the value will be on the bottom curve if \(a = 2\) the value is undefined if \(a >2\) the value will be on the top curve

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1__________ for 2) \[ \lim\limits_{x\to 1} \frac{x^2 + 1}{x  1} \] the value is undefined as we are trying to taking the limit at the asymptote

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1i hope i haven't confused you too much

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0noo u havent so i'll do the same this with lim x> 1 (x^2 + 1)/(x 1)

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1another way of saying the value is undefined is to say the limit does not exist

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so i'll do the same for lim x> 1 (x^2 + 1)/(x 1)?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1yeah, i would use x =5,4,3,2,1,0,2,3,4,5 this time

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1ok im off, good luck

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0hey so i did it is this correct? dw:1359335654116:dw dw:1359335759751:dw

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0@satellite73 can u help with this?
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