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asnaseerBest ResponseYou've already chosen the best response.1
have you attempted to sketch the curve first?
 8 months ago

FutureMathProfessorBest ResponseYou've already chosen the best response.0
dw:1375034315072:dw
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
which part are you stuck on?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
how do i sketch if i dont know the points
 8 months ago

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

mathcalculusBest ResponseYou've already chosen the best response.1
i can't use calculator.
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
ok  lets break it down into smaller steps
 8 months ago

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

asnaseerBest ResponseYou've already chosen the best response.1
so lets sketch this...
 8 months ago

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

FutureMathProfessorBest ResponseYou've already chosen the best response.0
Its already been sketched btw
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375034583963:dw
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
ok how did you sketch that ? :(
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
I 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
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
we 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
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
so the actual line should look like this:
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
does that make sense?
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375034970995:dw
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
so when are the times that we fill in the dots?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
and don't fill in?
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
you 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:\[x<2\]\[x>2\]
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
note that the first 3 INCLUDE the point x=2
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
if that makes sense, then we can move onto the next part...
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
so stoping at two we fill in
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
and whatever is greater than 2 we leave alone?
 8 months ago

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

asnaseerBest ResponseYou've already chosen the best response.1
so first lets sketch f(x) = 1
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375035727853:dw
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
wait, can't we sketch x=3 because it says x is GREATER than 2
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
now 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
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375035852984:dw
 8 months ago

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

asnaseerBest ResponseYou've already chosen the best response.1
the value of f(x) = 1 for x greater than 2
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
that includes points such as x=2.000001, x=2.5, x=3, x=99, etc
 8 months ago

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

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375035980350:dw
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
oh okay so i can use 3.. great
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
so now we just combine both parts of the curve to get...
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375036030210:dw
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375036145535:dw
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
good. now we can examine the lmits
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
the 1st one is limit as x tends to 2 from the negative side
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
so  look at the curves and see what you think the answer should be for this case
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375036264164:dw
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
why is it 1 and not 1?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i see it's coming from the left side and the answer is going to be negative.
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
why is it going to be negative?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
but where do i look, in the y?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
because it's coming from the left?
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
lets approach the limit in steps
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
how do i look for the limit when it approaches to 2?
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375036393036:dw
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
dw:1375036417600:dw
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
can you see now what the limit should be as x approaches 2 from the lefthandside?
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
perfect! well done! :)
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
now try to do the same for x approaching 2 from the righthandside
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
right side of 2 it approaches at 1
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
bingo! you're a pro now! :)
 8 months ago

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

asnaseerBest ResponseYou've already chosen the best response.1
I believe you have grokked this now! :)
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
because, it's not coming from either side.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
omg thank you!!!! :))
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
thank you so much!!
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
yw  I'm glad I was to explain it well enough for you to understand. :)
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
i'll apply this to the rest when im doing a problem
 8 months ago

asnaseerBest ResponseYou've already chosen the best response.1
perfect!  keep at it  you seem to have a natural ability at this. :)
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
What if they tell us to calculate instead of sketching?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.1
do we simply substitute?
 8 months ago
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