leader: becca math 166 section 8.1 supplemental i ... · leader: becca math 166 section 8.1...
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Leader: BeccaMath 166 Section 8.1Supplemental I nstructionlowa State University
Course: Math 166Instructor: Dr. Martin
Date: l0l9l12
Find the Indicated limit. Make sure you have an indeterminate form to use L'Hopital's Rule
1) l imr-s
A\ r . COS fZ) llTfl--n
-/t-x
A\ r . x2+6x+8i) umr+ _2;44
2 -Co:x = 2_ I ,EZx-sinx
9- r/o {.'h= {^ir^
v)O
z/ -Sth x
- l
*t[ '"= {r'n^
x) -2=E
!r/xs -3xz +x4) limr-s x3-2x
g =f-!L4
.\
-z-tu\t^x)o
=S : inx 'E
2x'b2x -3
3x2- tox * I
3tz-z
1060Hixson-Lied StudentSuccessCenter * 515-294-6624 .!. [email protected] * htg://www.si.iastate.edu
c/o-
5) l imr.,o
6) l imr-,.
ex -e-x- 2sinx
^ x ^-r(C+C
zcos xl+ \ E
\J-=TJ,[ t- t2
. [ t l t r ^ .lLwnL)!
\^-
- , /+t- : Lvz{ t
-c
lnt
\"
7) l im"-o ex -ln(t+x)-t -7;
x2 ry {,ntx)O
o\\ r-r-rrnx)o
xli+x
z\
.-x \tr + (i-'\'
\l_* \-r I
2_i '_ --l -4 iI - I \
Leader: BeccaMath 166 Section 8.2Supplemental I nstructionlowa State University
Course: Math 166Instructor: Dr. Martin
Date: l0ll0l12
Find the Indicated limit. Make sure you have an indeterminate form to use L'Hopital's Rule
l) lim'-- r(10#{- r,) = * t U u^Irbo
-* (m*c--)e hrcal?
ux ,0nx' i *,: I,,'rn
y-rrF ioOdtLDxrg*
= -0:t'nX)ro
3i16orte))l()o+e^
={I/\:
"1,\h
-_w\f {.rir'\
x)!"
W,rv.'x+\p
300 r3ex e, . /e"
w=tr2csc2 x2) l imr-e cotz x
'* \Ju L' Itdgito.l s C^rq \tl,ru
3) lim.- I (tan x -\P-
"il*in*
=Luiu # s,4a's-@- =g R"k^
S,-x; 4l"im
x)o
--B?
-c6-x
sec x)W"/tvncnun wrnn
"0tnx)Pz
j'9u*\)ga
Sinx-ttosx=s, H.
caMrvfro^ dltuvtu/vrw
=z(o
ffix bsg= G* S\ng, \
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*fOf V4.'( *5rO) lim'-s ( cos r )cscr ,*/= I so ttlt- l.v\
tg_In ur U.(cosx)tsc*"l,rn3,-01^(Ss\t** @-'{./l $ " csx-0ncosx ,[e ux- u$,vtt o-ercuruy,1
H r'rlrg 'S cxx orrosx-0t/$t\x)o {u.g
-erg
: -01/i^^\f)o
-r'tV rQ,\h-+ O-
Lncosx lu0r\2 cr.x't-*SWrX
U,imxto
. \.-. [-Sins/\CUSX
CIBX= s #',# : 0ta,vr
x)o-$n\ _.o _^. ,osa - I -u
15) limr- * x7
,>\u-.t s= x"l,tng " -2sn
:b 4J"S =O*"03:-9,
H3' vf (*^
: * i =e
tAru- g ;eK$,tOut 1D b6t^^ s'cttA
6cI rrC&Xu^Qosx; = L+o
"0lrr\ - YJ-Tw,OJv\A
\)o
"ttng -- i o,tn* e \^,A,u,t t{qnfiroa-
-0uq = Orivn- xlb
0\.r l r^ . t . ln "r i
&vI tJXAF\
hs 'o So 9=A_Lx
lnx\P - v /* qe ar/Jvtwltu\ dl^lto(Yrinatut
t[lx+l
:AlfnY.)x
lU,r\,]-Ib..\'S.t")l,lnv\ g-r)hrx
0rny- ytx-il __lrm
t-ill,yrx \raJnv -xtnI
[r-r)[rryI
I -zx rl----lnx * [x-l\- z-.Jff'(/'ttc*^p.st-o_
: - jo+2
*-zr*t= ltz*->,.- x
,gr '2bo? -Li\nx+1.
| ^,n*q h "\
-{ri,yt I -Zxz+v \n rx)L x /\ :-or,tn l-zr2+y
gr..* \-xi x)a G;] .- , /b
Dt "l.umx)a-4v*\.0,rnx+ xLi\ +t\---V-/gofuir* gr)\"t
Math 166 Section 8.3Supplemental Instructionlowa State University
Leader:Course:
fnstructor:Math 166Dr. Martin
Date: l0/l4l12
Calculate the Imnroper Integral or show it diverges:
l) l]- eLxdx :6'. \'eotr* ili"or)6 - o\
|d.r, = d,
: liY\ q,,0)P io
= U)i^ Is)ro AC
({\ e. d,,,
I" ,1I
e+" \Ya
J- , ;4.)\ - 4" /
:-{,wn _lhrbo .4
-,!N" { |o.* L?
'- -b,I^ /r .+ * \a+n \4 - 4t
DI :# : /r,rn S: # .k d\: -! g" S,t i'^'l*=# gi { ' .2 \ '=#{K(zo'-z)
\r\r\Ai./r^ XOeS nr tSo 30 ,n @
1060 Hixson-Lied Student Success Center * 515-294-6624 * [email protected] .:. http:/ ^
vw.si.iastate.edu
3)fifta* (,lr: ltxzdJ/u' Zxdx
trdu' Yd,x
nt x=/ ,n \of fo"
=g \,+ k")d*b)p ,a 7 t
'n g )-o^t,^t .|
'Y !"ut r.*\ ft0
=S ti^lr*f, \ -+-ora \ror \
q I:'#o* T%,-- {j/r\b-' tto
: lsnnfe)w
: Ql,f,Ab) rF
- jarlfv\u)re
:.t ri,"l\oD\s
Ph\unqu.sro\ASs-rb[Df-,tJr{ j- \ .
h* l-l)-lbb. +
b
-{Bb ,b
-v-b
dx
;dx
Li)d'rf-rX'
.1r b( lb
) tt'
HI.t-\-uLX
Tfe0tA
t- 'F.
0A€e
.Le
r r - - i - t=Z
E 0rM^ q& _ br,n ,nob)!A 15 6{,L,a^-2$v
UIL Lr tt6Piur's P.u\r.
er;rn LJc,s,wT
Le.
{;1>lz- l
t - ' l
s) J: #(usetrig substitution)
Vtl* rilto Z rvrv4r4,ts ' [D* CD\F
D\ dx.=J &'*ro)"o
ab /x\-Jo (x2*uoT{a-a.no
-*A,y,rz""p' *'* &)
,^o dto \ f f i-\p
o
I-a
;Lt{v\t')^p
: !.Jn\i\P
\'\ft\\P
4
D[x -- Asefede
o , l " \*n i ' ( i ) \ -7 ( f ' 'o I
-o,; 't'l'l^AA)*
I
rz8
t-Ft
- lrzt
= QI,,/tt0.)\P
> -bi/AA)UA
){7o
=l.urr'n'-fb)F
\r.. d
+setlgoc,@1b s ss'.s d6
) zlo :m4O)l_.0
- xtb=Urfrt 'Q L..1- d'ab)F \ to. t*
>2b
. r-P:.Qjaryr
-\ggfe db
b)F [ ' ' )
Lo) - hun P"\ L$'# [t)
- r Flf\ - l'l'oo,
-*Oa Lz) iz t7)
z5v
= -t unnb)F
*p\k- j " - a
t.!rrmb)s
'-0li,nnD\P
:,[ir,msv
' y U$ t, tfr') *v*o f wdertar':Q,Ju;?:Jv b)'
'X gs i,#o 50 o=E
'I\cb\1r15qr,$CoSe \w"
x70
s
:0f^e-0a CD u\^\I f
ffi3**)'
fuoe, uxl/i'(- \P
e.Q- \\---{
Z5o
=Tt'Jo
p*t^' 5in?'6-- Zsrngtose
Furu, /, *YSivro'k '
roSe' tffio
-4- fl*-t"
b-- kctw'G\T-ftu,n'tl\ #^fr)@o
5't) .
'H.h *r'G).*;; tft\f=yS fitnw'L%\ t (tr).u