anonymous
  • anonymous
@asnaseer finding the limit:
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
1 Attachment
asnaseer
  • asnaseer
have you attempted to sketch the curve first?
anonymous
  • anonymous
|dw:1375034315072:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.