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UMB - MATH 0132 - Study Guide - Final

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math 220, Fall 2013, Final Exam

gf'-fe 12) fx) = (x + lnx) lii) f(x) = seva 1ii) f(x)= 92? chain rule: f(g(x)) g'(x) f(x) = x et = (x2+1)(-_**)-(-x)(2x)

Don't forget about the age old question of What is the difference between diabetes 1 and diabetes 2?

product Rules

(x2+1) 2 f'(X) = 3(x+ lnx)(1+) fig+fg' If you want to learn more check out What are the causes of marijuana?

- (x) (etx)= xoa ceva)

21)y = 3X+2 = f()

=(1)(ex) + X - eJx. dx TX 272) y = x2 + 4x+1 > Y2 = 2x+4 f'(X) =3

evt + Xerx (2) x 12

y = 2X+ 3 7 y = 2 f(0) =3(0)+2=2 etto xerx ( 3 ) ( ) 2x+4 = 2 + 2x = -27X2- f'(0) = 3 Don't forget about the age old question of What are the nine characteristics of living things?

Y= (-10%+46-1) +15-2 +6-1,-2)

Our

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SOU

02333 15111-3)=-2

x(x-3)=0

> x=0,3

35X24

: 1.75

YEO Top

Test point: 13 y = x(x-3), x-axis : y = 0, 0<x<4 41) 5x+1 dx 423) / J1 + 4x dk Don't forget about the age old question of What is alexis de tocqueville known work?

ten154+1/+C SC1+4x)l2 dx no n solta) - gex) dx

5-3) -S860-(x(x-3) dx + S3+ ((x(x+2) - o)dx

- 3 (1+4x3/2() - S• (-***3x)dx = S3 (x®-3x) dx

= 1 / 2 (1+ 4x } 12 = 1 / 6 (1+4x) & C Article vivative : - * A+ X:33 - 183093 2099-0 4ii) S. [ ezx 10 dx At x=4; (439.3440*- We also discuss several other topics like How do you determine electron density?

Sole-2x + 10) dx At x=3 =1598.3439

anticleriventive: Že=2x+10x10 Fb -Fla) -30

(48211_1001) - (- 3620_1060) - Žé :10-

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VSO Don't forget about the age old question of What is the holistic approach in anthropology?

8000

v=x2h=8000

m'=0

be *2012

(20)

h = 8000

constraint. V= (x))(h) M = 2x2=4x 20)

V=X2 h=8000 Base : x2, roof :x?, sides:4(xh) =2x2 + 32000x1 material = 2x’+ 4xh s objective M' = 4X-32000x52

4x - 32000x-2-0 he 9900 4x = See on

h = 20

x3=8000 Base: 20 x 20 cm

x+2020

. height: 20 cm

Studyse

Math

220

Fall 2013

Conta

_

6i) P(A) = Poext

7 = 20e-410

(ln(4202)

( 4= 20e

1. 20

-10%

se (en (1/20)) +

Sour

e

I ents) = (en (7120)}t

en (20) = -10x x = ln (7120)

en(115) (en(1/20)

alo

tenas

- 10ln (15)

en (7120)

9 same as (10005) / ln (20/1)

Study SOA

71) 5(8,4) – y? (9x+5y)" (0St442 9x54%(a) = 36y2 (9X+54)

677) y = f(x), f'(X) = exit 3 + 2x, f(i)= 0

(ex-1 + 2 + 2x) dx = ex-1 + Inx1 + x2 + C f(1) = ''+ en 111412+C =0

=ľ°+0+1+C =0

1 + 1 + c = 0 -

0 : 2

by (zwy? (2x+59)*) -> use el figufg!= (124)(98+54)*+ (36y?%Ex9x+54)/(5)

syöx 72419x454) 540y? (9x754)

f(x): exalten 1 x 1 + x-2

For and derivative Testi

7) f(x,y) = -2x++zxy-y* +48-604+5

Đx - 4x + 2 + 4

2x - 2 = X-3

a2f

dy. 2x - 2y - 6

X+10

Sy2 - -

X:-1

e

(2X-24-6) =2

-4x+2y+4=0

2x-24-6=0

2y = 4X-4

2X-6 =24

Y = 2X-2

Dexys

y = 22-2

y = X-3

0(-1,-4) = (-4) (-2) - (2)2

y = 2(-1)-2 = -4 (x,y) = (-1,-4)

-420, 50

(-1,-4) is a max

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