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