Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

limits

No description
by

Sarah Luken

on 30 August 2013

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of limits

limits
DEFINITION
examples
FIND THE MAXIMUM AREA OF A RECTANGLE
in a rectangle with a perimeter of 24,

2w + 2l = 24
l = 12 - w
A = (12 - w)w
= 12w - w²

Limits That Do Not Exist
left and right
unbound
oscillating
basic limits
sally luken
ap calculus

If f(x) becomes arbitrarily close to a unique number L as x approaches c from either side, then the limit of f(x) as x approaches c is L
https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&docid=C94gY325gnzVeM&tbnid=fP5QdiFR30nTkM:&ved=0CAUQjRw&url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2F(%25CE%25B5%2C_%25CE%25B4)-definition_of_limit&ei=26AeUorRBZOw4AO5lIGIBw&bvm=bv.51495398,d.cWc&psig=AFQjCNGTHvAe-jkWycaAHOJLYDphlUvL2A&ust=1377825369309464
12 - w
W
the maximum value for A is when w = 6
"the limit of A as w approaches 6 is 36"
lim A = lim (12w - w²) = 36
w-->6 w-->6
http://www.google.com/url?sa=i&rct=j&q=the+limit+does+not+exist&source=images&cd=&docid=SAcgB1Sh6zfWlM&tbnid=jPy1Sx2Ri62uiM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.tumblr.com%2Ftagged%2Fthe-limit-does-not-exist&ei=SK4eUr_oDdKz4AOC5oHgCg&bvm=bv.51495398,d.cWc&psig=AFQjCNFOx0QBeu4P4m1ebNCZ72BXdrPN9A&ust=1377828753140342
EXAMPLES OF NONEXISTENT LIMITS
lim abs(x)/x
x-->0
lim sin (1/x)
x-->0
http://www.google.com/url?sa=i&rct=j&q=the%20limit%20of%20the%20(abs(x))%2Fx&source=images&cd=&docid=-DxXH4TQS_5hDM&tbnid=cqwBE7_yoSRsaM:&ved=0CAUQjRw&url=http%3A%2F%2Fmath.stackexchange.com%2Fquestions%2F28268%2Fwhy-dont-these-limits-exist&ei=mL4eUuOpE7TJ4AO6iIGgBg&psig=AFQjCNEgCDQdtEVMMFrbFumoxRDVuzZhWg&ust=1377832956229899
no matter how close x gets to 0, there will always be both +/- x-values that yeild
f(x) = {1, -1}

SO LIMIT CANNOT EXIST
http://www.google.com/url?sa=i&rct=j&q=lim%20sin%201%2Fx%20as%20x%20approaches%200&source=images&cd=&docid=RhkLcEHtXv5TeM&tbnid=4pPvJ39WWrkpWM:&ved=0CAUQjRw&url=http%3A%2F%2Fwebpages.charter.net%2Fmwhitneyshhs%2Fcalculus%2Flimits%2Flimits.html&ei=isAeUriVDbTF4AORm4A4&psig=AFQjCNGrsdi2R8t57ilbQZtMmq3t8z4Mqg&ust=1377833449871581
no matter how close x is to 0, you could choose values of x that yeild
f(x) = {1, -1}
http://www.google.com/url?sa=i&source=images&cd=&docid=jllMcAsBqB9gNM&tbnid=BO-dXsuj7aO-sM:&ved=0CAgQjRwwADhR&url=http%3A%2F%2Fwww.cliffsnotes.com%2Fmath%2Fcalculus%2Fcalculus%2Flimits%2Finfinite-limits&ei=Jb0eUuH4AtS5sQT2zIC4Cw&psig=AFQjCNG3Jw_RAOv_JyGlUNOk5JuE_GMyLA&ust=1377832613112152
lim 1/x²
x-->0
because f(x) is not approaching a specific real # L as x approaches 0, you know that the limit does not exist
the existence or non-existence of f(x) at
x=c has no bearing on the existence of the
limit of f(x) as x--> c.
let b and c be real #s and n
be a positive integer:
1. lim b=b

2. lim x=c

3. lim x^n = c^n

4. lim √x = √c

x-->c
x-->c
x-->c
n
n
x-->c
estimating limits numerically
CONSIDER : lim(4x-2)

x-->2
from this information you can estimate that the limit is 6
so : f(x) = 4x-2

construct a table with
2 sets of values for x,
one from the left and
one right
the end
http://www.cengage.com/resource_uploads/downloads/1111427631_267947.pdf

http://www.mathsisfun.com/calculus/limits.html

http://archives.math.utk.edu/visual.calculus/1/limits.7/

http://www.rootmath.org/calculus/limits-that-fail-to-exist


and the assistance and approval of Nick Luken :)
as x approaches 2,
f(x) appears to approach 6
https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&docid=2g2sf8Nz2M1szM&tbnid=DmONayTrIwGF4M:&ved=0CAUQjRw&url=http%3A%2F%2Fminimalshirt.spreadshirt.com%2Fkeep-it-simple-A7841883&ei=FgUgUqSfO5K24APrhIA4&bvm=bv.51495398,d.cWc&psig=AFQjCNEt71Vcg9Wer0go_f7Kt7ftvw1dhw&ust=1377916535277990
Full transcript