m€¦ · ↳ thingy few if Oc Lex Then both converge or diverge Ilytcu fiiE " " Fs Fatso. 't I....
Transcript of m€¦ · ↳ thingy few if Oc Lex Then both converge or diverge Ilytcu fiiE " " Fs Fatso. 't I....
m :¥Last day P
-
⑧ p④
④ Converge or diverge §
⇐,
KIIT,
= Ot # t It . . .
I::t::h¥rETSince { heftyand I ÷ are series
with positive terms,
we can usethe limit
companion test .
thin.
him .Hkh¥h= Lino h.EE#hi;.fe=iIo=I
Since OL L L,
either both P⑦series converge or both series
diverge .x
Since I th diverges ,so does { k¥74
ke ,
b- I
-
④④ Calculate pros , Cui ) and scalyhit
Ii = C 3,3 ,
-37,
5=51 ,-1,27
pro hit =Fi . ET-
scalp tu )
ii. T= (3)(1) t ( 3) C- Ht C - 3) C- 21=6Tp¥hit THEE =D → hitseahihit-EF-FT-rf.ph' - ' 4 '
'"
7.8*410 ⑤④ !Ex d x = fine
, o+ fiEr
Is ¥,not""
hi =
fine.
E E- a J
= 2 e- 2 e
°
= 2e①÷÷÷÷÷÷÷÷i÷÷÷÷
④ ±w* p④x
④ EC - 11k¥.k=O
Could use ratio test,but in this
case ,its the geometric series .
-
E. hi En. E. Est
i
Nst p④
) tanmcx ) see" ( x ) dx where m is odd
MH, n> I.
• take out one see Cx ) tan I x ) and save
it for du
• rewrite the remaining tank ) 's in
terms of Tedx ) using
It tan' Cx ) = Sed Cx ,
• Set u = seccxl ,du -
-
seccxltancxldx
-
E ftanslxlseicxldx= Stan
" I x ) Sec 4×1seccxltancxldx
EinoTE
Sec C x ) 's
= ) ( tan' Cx ) ) 'seicx) seccxltancxldx
= S ( sectx ) -
I)2sec4x) see G) tancxldx
=f(sec4xt-15seckxlseccxlto.mx,d×P④=p) ( u '
- IT vida -flu '- zu 't 1) u2 du
dYY¥!tana =f(u6-
zu"
tu'
) du
= ¥ - 2¥ + It C
=seg_zsgtI{If
tatyana p①{ an
,Ebu positive terms
↳ thingy few if Oc Lex
Then both converge
ordiverge
IlytcufiiE" "
Fs
Fatso .'t I