Covers most of calculus 2 along with application problems. Topics include: integrals,

Math 11B 2 – Covers most of calculus 2 along with application problems. Topics include: integrals,

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University of California, Santa Cruz

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1–3 1-+ → • ¥+ – ¥ 3 O→• =f(¥, +7-3)d×=×¥,d×+f¥zd× = 2 ¥, dxt-3x-s-dx-zu-dui-3ftuduz-zlnlull-3/UzltcU–x-3U=xtl du _-d× du=d× =zln 1 ×+11+3 In / ×-3 / 1- C 5 ×- exzzy?y,t3-gMg – 5 ×- = A(× – 3) 1- Blxtl) 1 ×1-171×-3) Cx+i)(×→)- = 5 ×-3=1-1×-3) + Blxtl) (True for any × Plugin : ✗=3 → 5131-3 A B. • 13+1) =l B=¥ = Plugin :x= -1 → 51-17-3 Al- 1- 3) + BIO) = -8 = -4A A- = -1-1=

Plx) I Qcx) deglp )=3 > 2- deg LQ) 1) m%±ʰ

  • x – G ✗ 3 – 4 ×-10 ✗ + I = Quotient ~
  • ✗3- ✗ 2 – Gx / ✗21-2×-
  • X2 + ✗ + 6
  • I 3 ×- (Remainder Quotient ~ ✗3-4×-10=1×+1) (✗2- ×- 6) + (3×-4) ~ Remainder = ( ✗ + 1) (✗2- ×- 6) + (3×-4) ✗ 2- × – = 1 ×+4*1-6) 3 ×- É + ✗2- × –
  • = 1 ×+4+3 ✗×2–4 ×-
  1. = 3 ×- % [(✗+ 1) + ✗2- × -6 ” =S’◦c×+nd×+%¥→ =lÉ+×) ]! + I = (E) -0 +I 1- =/ ‘ 3 ×-4 B O 1 ×-371×+2) = + ☒ s ¥μd✗= lnlxtkltc 3 ×-4=1-1×+2) + BIX-3) *= -2 31-27-4–0 + B 1-2- S¥±μd×=÷enlx± – 10=-5 B B- _¥ B= ✗=3 3131-4=1-13+2) to 5–5A → A= =%d×t2×÷zd× = ( lnlx- ) + 2 In 1 ×+21) ]’ ◦ = lnl-2 / + 21h13)
  • (lent-311-2 In 121 = lhztzln 3
  • ln3t 2hr =3 lnztln 3 1h3 – 1h2 = In }

gb ¥ dx =f × ” d. ✗ 1 = ✗ -2+ = → ×

  • l = – ‘ × = – b- – (- ÷ ) ‘ = – b- + It
  • → [ 1 , XD
[

“” “”” ” “” ” “”” ” ” ” ” 1

SE ± dx = him b → a S b b → a ↓ % , ,, “linen in = . ☆ The integral SEE dx is divergent & ¥ d ✗ = In 1 × 1 ] ? ‘ = lnlbl r

T

:

i + ✗ ad” = % ¥ 2 + [¥×z dx

  • x f- eims: ¥. ax + him 5b¥ d ‘ tan- ✗ Ta tan
  • ‘ × ]!
  • = him ltario – tan”a ) + him (tan – ‘ b- tan-10 ) a→- x my b. → x T

“”÷¥✓

= him a-• 1-tan – ‘ a) + him (tan_ ‘ b) b. x = – l- E.) + Is = E. + % – – Is

fly)=e – x “- *1- fay i even U pg,y=e-t¥é×z function fcx)=é× > → even function dx=JF

ⁿh?”

“”” ¥ S?éñ dx=TÉ $ %r×e

  • (E) 2
  1. e- ¥ 12 go ax we
  • ✗ 2 d✗ d. × =S?•é”d× + SEE”2dx a- Tx du-j-s/oe-u2U–¥ 50 d ” ☆ ☆ =L;m ‘ 2J×du=d× dU=¥d×ñ5é ” a→ – • Fae_ ” dxtlimgb du =Tz.%I=T “” ” 2Udu=d× ” “

§

*d”=d× ×=o→u==o slim ✗ → am -5!é%xtlimg?é”d× – =u=→, ☆ ☆ b- • • * •

{

” “” “” “

####### *,mxn•_

☆ ☆

Cmj

Read pages 390 ~ 392

☆ ☆ ☆ ☆ a b 1 fave = 2- c- is [ ( It ✗ 2) dx = } ( ✗ + ÷ ) ]! = } ( 2 + ÷ ) – I

  • I +%) ] ?÷ (2+5+1+5) –§=2[ Lund ↓ – t /SO [0,30] Se at Tane _- ¥ 5%120+e-%) dtS e-‘”◦ ᵗ
  • I/ so e- It +C % ( 204*
  • so,e- “so ]% % (201301+751-50) É “”) – ¥ (0+751-50) E)

F- Tave •• ••

17 (6) Infection f (t) = – t level(t – 21 of) the (t + Meas1)els virus

what 1- = days is the average level of Infection ? fave = z!-o 5 !fit) dt = ¥ 5 }' - t (t -21) (t + 1) dt

B. 1Wh ¥

Math 11B 2 – Covers most of calculus 2 along with application problems. Topics include: integrals,

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