-Tr+e, Au e.esee, Be.l*^rue.
pG.) =. .c:
Fi*.A U^. eueloql q".o.Aio*k ov\
U^e- c.r-rvq L-\S*"^S [l^e-
Po\hks ,^rl.*o. }C - t or J
4,. t\-A = trts - PLil
-- a-l
3-t =B
a_
- b-> PLe) = t'=t
:-
trcil = I =l
AS' u.!€- h\ov€- O-*o^"lJ , t{^.e- Crr.rrx- t{^e- <
G.ve,}erq
Xt*A,e*-E L-t.^reo-'- *t J po\..-\: -L.o.-.n : .{
A" t-*J he.t.^*",^. A c,^J B
= _L[=-+L) - FC--)
x- -Lk -:c
Pt .+t-.\ - F t-.)
h
G.d .r A' S c.=J //lt,* dorivq}tip
Q'n<'t;on
Q-x..-,.^pLes l
t. Ptq = i.-'- a-tc- . trl'-d U^. o.\rabqXq 6\r\
AF*A\e^k
Pt=) tet.-.r*-er^- t\^* rto\xls
I
rc=- I o'r^J :c= \ .
a-. ., Co-) : 3--c + f,x-' . t-i,^d. H^e- eve*e.tq - F-I- "N
r0
c}.re. r"..q
q
c- So. U^e \o-k "..-L
rc-€ L- i.' *aJ
.S DC=) = - a=3
F> I\"]<-tr,. :,^e- + (tr-+ri - PLa) G) \.$€>p*I erJ.\E\^,q}
{*
U*.
tL n^bA aJ +t. tri-^J o..Lr .
Xr*Ate-k ov\ ir^-\<.^ro[ :ce f.]; t+J
, LIh{ITS
f (*)= * *z
Determine: trq(x+ z)
We can see from the graph *rat liq(r + ?) = q
..3x+L
lrm- 7
r--+i --
4X 8
(n thee examples we may simply substitute)
Be careful of &e followine;
Zero Denominator Itrfmtty
x'-9 116-
3x-2
ltm-
r-+3 y-]
lVe carmot merely substitute as
thedenominatcr it 0 x+6 4X
3x2 )--.
)
= 16
(r + 3X' -:) x
x+3 X -3 = x.lim-ll--
p 4X
rL
Iim
= r-)o
4
=limr+3=6
x+3 1
We knorv that iim- =0
l+o -Y
E)GRCISE 2
Determins each of the following:
1l; lim2x (2)tim3 -x (3)lim{2
" - x)2
r'+3 -t+i x+J
x: -4 \', xj
,.
(4)lrm-
J
(5) Irm- (6) Ilm_ -8
:--r0 ;g
' x+2 'Y r->2 r-?
1g
-/
(9) hm x2 + x-2
\(X) ltm
-. xz +3x-4 -\r-1-
' - (8) lim-:--i
x-r0 ' 's+-2 4:r+8
\r, x- -l -tr - )
\4x 2x1 -3x+1
*qS* fN) hm
'\r+*ZX-l fl2) hm-_=-
r+@ 3X" -X+2
pG.) =. .c:
Fi*.A U^. eueloql q".o.Aio*k ov\
U^e- c.r-rvq L-\S*"^S [l^e-
Po\hks ,^rl.*o. }C - t or J
4,. t\-A = trts - PLil
-- a-l
3-t =B
a_
- b-> PLe) = t'=t
:-
trcil = I =l
AS' u.!€- h\ov€- O-*o^"lJ , t{^.e- Crr.rrx- t{^e- <
G.ve,}erq
Xt*A,e*-E L-t.^reo-'- *t J po\..-\: -L.o.-.n : .{
A" t-*J he.t.^*",^. A c,^J B
= _L[=-+L) - FC--)
x- -Lk -:c
Pt .+t-.\ - F t-.)
h
G.d .r A' S c.=J //lt,* dorivq}tip
Q'n<'t;on
Q-x..-,.^pLes l
t. Ptq = i.-'- a-tc- . trl'-d U^. o.\rabqXq 6\r\
AF*A\e^k
Pt=) tet.-.r*-er^- t\^* rto\xls
I
rc=- I o'r^J :c= \ .
a-. ., Co-) : 3--c + f,x-' . t-i,^d. H^e- eve*e.tq - F-I- "N
r0
c}.re. r"..q
q
c- So. U^e \o-k "..-L
rc-€ L- i.' *aJ
.S DC=) = - a=3
F> I\"]<-tr,. :,^e- + (tr-+ri - PLa) G) \.$€>p*I erJ.\E\^,q}
{*
U*.
tL n^bA aJ +t. tri-^J o..Lr .
Xr*Ate-k ov\ ir^-\<.^ro[ :ce f.]; t+J
, LIh{ITS
f (*)= * *z
Determine: trq(x+ z)
We can see from the graph *rat liq(r + ?) = q
..3x+L
lrm- 7
r--+i --
4X 8
(n thee examples we may simply substitute)
Be careful of &e followine;
Zero Denominator Itrfmtty
x'-9 116-
3x-2
ltm-
r-+3 y-]
lVe carmot merely substitute as
thedenominatcr it 0 x+6 4X
3x2 )--.
)
= 16
(r + 3X' -:) x
x+3 X -3 = x.lim-ll--
p 4X
rL
Iim
= r-)o
4
=limr+3=6
x+3 1
We knorv that iim- =0
l+o -Y
E)GRCISE 2
Determins each of the following:
1l; lim2x (2)tim3 -x (3)lim{2
" - x)2
r'+3 -t+i x+J
x: -4 \', xj
,.
(4)lrm-
J
(5) Irm- (6) Ilm_ -8
:--r0 ;g
' x+2 'Y r->2 r-?
1g
-/
(9) hm x2 + x-2
\(X) ltm
-. xz +3x-4 -\r-1-
' - (8) lim-:--i
x-r0 ' 's+-2 4:r+8
\r, x- -l -tr - )
\4x 2x1 -3x+1
*qS* fN) hm
'\r+*ZX-l fl2) hm-_=-
r+@ 3X" -X+2
