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mathcalculus
 2 years ago
@asnaseer finding the limit:
mathcalculus
 2 years ago
@asnaseer finding the limit:

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

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

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

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

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

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

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

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

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

mathcalculus
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0Its already been sketched btw

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

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

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

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

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

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

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

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

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

mathcalculus
 2 years 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
 2 years 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

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

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

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

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

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

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

asnaseer
 2 years 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

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

mathcalculus
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1why is it going to be negative?

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

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

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

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

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

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

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

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

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

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

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

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

asnaseer
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1i'll apply this to the rest when im doing a problem

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

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

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