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1 Attachment
have you attempted to sketch the curve first?
|dw:1375034315072:dw|

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Other answers:

which part are you stuck on?
how do i sketch if i dont know the points
all i see are x+1, x <> 2 then im stuck
i can't use calculator.
ok - lets break it down into smaller steps
first, you are told that:\[f(x)=x+1\]if \(x\le2\) agreed?
yes
so lets sketch this...
so for a) since it;s coming from the left side it must be negative... and we use the top function, correct?
Its already been sketched btw
|dw:1375034583963:dw|
ok how did you sketch that ? :(
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
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 filled-in dot at that point. it needs to be filled-in because it INCLUDES the value at x=2
so the actual line should look like this:
does that make sense?
ohhhhh okay :)
|dw:1375034970995:dw|
so when are the times that we fill in the dots?
and don't fill in?
you always fill-in 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 filled-in:\[x<2\]\[x>2\]
note that the first 3 INCLUDE the point x=2
if that makes sense, then we can move onto the next part...
?
yes :)
so stoping at two we fill in
yes
and whatever is greater than 2 we leave alone?
i got it..
ok, so 2nd part of the curve is defined as:\[f(x)=1\]if \(x\gt2\) agreed?
yes
so first lets sketch f(x) = 1
|dw:1375035727853:dw|
wait, can't we sketch x=3 because it says x is GREATER than 2
now here we are told that this part is only valid for \(x\gt2\), so we need to draw a circle (not filled-in) at the point x=2 and throw away everything to the left of this point
|dw:1375035852984:dw|
yeah but wait, im not sure why we are using 1 when we can use 3 since it says x>2
the value of f(x) = 1 for x greater than 2
that includes points such as x=2.000001, x=2.5, x=3, x=99, etc
i.e. ALL points to the right of (and NOT including) x=2
|dw:1375035980350:dw|
oh okay so i can use 3.. great
so now we just combine both parts of the curve to get...
|dw:1375036030210:dw|
make sense?
|dw:1375036145535:dw|
got it
good. now we can examine the lmits
ok :)
the 1st one is limit as x tends to 2 from the negative side
so - look at the curves and see what you think the answer should be for this case
|dw:1375036264164:dw|
1 zt 2^-
at*
why is it -1 and not 1?
?
i see it's coming from the left side and the answer is going to be negative.
why is it going to be negative?
but where do i look, in the y?
because it's coming from the left?
lets approach the limit in steps
how do i look for the limit when it approaches to 2?
|dw:1375036393036:dw|
|dw:1375036417600:dw|
can you see now what the limit should be as x approaches 2 from the left-hand-side?
so its 3?
perfect! well done! :)
now try to do the same for x approaching 2 from the right-hand-side
right side of 2 it approaches at 1
bingo! you're a pro now! :)
2 is undefined?
the /tricky/ part now is what is the limit as x approaches 2 (without being told whether its from the left or right side)?
yes!
I believe you have grokked this now! :)
because, it's not coming from either side.
omg thank you!!!! :))
thank you so much!!
yw - I'm glad I was to explain it well enough for you to understand. :)
i'll apply this to the rest when im doing a problem
perfect! - keep at it - you seem to have a natural ability at this. :)
What if they tell us to calculate instead of sketching?
do we simply substitute?

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