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Limits Examples
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This works best in conjunction with the "Limits Notes on Examples" as that leaves commentary on these examples. Hence, these notes are free, as well as "Limits in a Nutshell" notes. It is to your own benefit to purchase "Limits Notes on Examples" and "Limits Theory" and download "Limits in a Nutshe...

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  • June 14, 2021
  • 12
  • 2020/2021
  • Other
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TUT 4
-




x C -
2




{
YET → axe ,

4 .
f Csc ) = ,


I cost ⇒ I x > I




a) Sketch the of f
graph

b) Determine the
following
limits
,
if they exist


i .
¥-2 f Cx ) ii LEO Six ) iii. ¥ ,
Stx )




;••€
I

#




?I
2=0
① f Cx ) =
← drawsereahiigshe line
y=xtz
* Check where line
straight

•
ta
↳ Vertical


it's
Asymptote




i
* Check where I i

' 2

. .
.
. - - ,
. .




£+2 = ate
- -2

I = C x -1232

It = x t2
4
vertical
← I where
asymptote
xt2=c
2+2=-1 straight line O
=


X = I =-3
x
the denominator
-




because it is in


L to
,
f C- D= Iz
=
I FC -
3) =
-31+-2=-1



PC -
I
,
I ) Q C- 3
,
-


D
* These are the

turning points




② fcx ) = 124 -
I
pal 1×1 -
I




=D
to !
% '

, ③ fcx ) =/ cost I




Cos X




period ⇒ it -




( Ex )
i

cos
-




period .
"¥
=L ,
radians




leos .
xD WIN
he - I L L,




x C -
2




{
YETI → a ski
Now combine the f Csc ) = ,
graphs
I cost ⇒ I x > I




• im
- -
- -
- - I




.




.
.
.

.

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