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mathcalculus
 one year ago
@asnaseer finding the limit:
mathcalculus
 one year ago
@asnaseer finding the limit:

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asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1have you attempted to sketch the curve first?

FutureMathProfessor
 one year ago
Best ResponseYou've already chosen the best response.0dw:1375034315072:dw

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1which part are you stuck on?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1how do i sketch if i dont know the points

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1all i see are x+1, x <> 2 then im stuck

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1i can't use calculator.

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1ok  lets break it down into smaller steps

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1first, you are told that:\[f(x)=x+1\]if \(x\le2\) agreed?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1so lets sketch this...

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1so for a) since it;s coming from the left side it must be negative... and we use the top function, correct?

FutureMathProfessor
 one year ago
Best ResponseYou've already chosen the best response.0Its already been sketched btw

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375034583963:dw

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1ok how did you sketch that ? :(

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1I just sketched y=x+1 got 2 points on it: when x=0, y=1 when x=2, y=3 and then just drew a line

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1we are told that this is only for x less than or equal to 2. so we need to CHOP the curve at x=2 and draw a filledin dot at that point. it needs to be filledin because it INCLUDES the value at x=2

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1so the actual line should look like this:

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1does that make sense?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375034970995:dw

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1so when are the times that we fill in the dots?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1and don't fill in?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1you always fillin the dots if the point INCLUDES the value  so all these would result in filling in the dot:\[x\le2\]\[x=2\]\[x\ge2\]and all these would NOT be filledin:\[x<2\]\[x>2\]

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1note that the first 3 INCLUDE the point x=2

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1if that makes sense, then we can move onto the next part...

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1so stoping at two we fill in

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1and whatever is greater than 2 we leave alone?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1ok, so 2nd part of the curve is defined as:\[f(x)=1\]if \(x\gt2\) agreed?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1so first lets sketch f(x) = 1

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375035727853:dw

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1wait, can't we sketch x=3 because it says x is GREATER than 2

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1now here we are told that this part is only valid for \(x\gt2\), so we need to draw a circle (not filledin) at the point x=2 and throw away everything to the left of this point

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375035852984:dw

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1yeah but wait, im not sure why we are using 1 when we can use 3 since it says x>2

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1the value of f(x) = 1 for x greater than 2

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1that includes points such as x=2.000001, x=2.5, x=3, x=99, etc

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1i.e. ALL points to the right of (and NOT including) x=2

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375035980350:dw

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1oh okay so i can use 3.. great

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1so now we just combine both parts of the curve to get...

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375036030210:dw

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375036145535:dw

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1good. now we can examine the lmits

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1the 1st one is limit as x tends to 2 from the negative side

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1so  look at the curves and see what you think the answer should be for this case

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375036264164:dw

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1why is it 1 and not 1?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1i see it's coming from the left side and the answer is going to be negative.

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1why is it going to be negative?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1but where do i look, in the y?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1because it's coming from the left?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1lets approach the limit in steps

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1how do i look for the limit when it approaches to 2?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375036393036:dw

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1dw:1375036417600:dw

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1can you see now what the limit should be as x approaches 2 from the lefthandside?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1perfect! well done! :)

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1now try to do the same for x approaching 2 from the righthandside

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1right side of 2 it approaches at 1

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1bingo! you're a pro now! :)

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1the /tricky/ part now is what is the limit as x approaches 2 (without being told whether its from the left or right side)?

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1I believe you have grokked this now! :)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1because, it's not coming from either side.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1omg thank you!!!! :))

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1thank you so much!!

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1yw  I'm glad I was to explain it well enough for you to understand. :)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1i'll apply this to the rest when im doing a problem

asnaseer
 one year ago
Best ResponseYou've already chosen the best response.1perfect!  keep at it  you seem to have a natural ability at this. :)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1What if they tell us to calculate instead of sketching?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.1do we simply substitute?
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