Chap02 Solutions Ex 2 4 Calculus

20
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Transcript of Chap02 Solutions Ex 2 4 Calculus

Page 1: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 2: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 3: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 4: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 5: Chap02 Solutions Ex 2 4 Calculus

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Page 6: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 7: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 8: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 9: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 10: Chap02 Solutions Ex 2 4 Calculus

\

5. If y=arclanx,,show\at

<1 +13);/‘+1-w’ -= 0

Hcncc ndlhe slalucs éfalf derivatives of y when x = 0

Sol.

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»> - “‘%‘l<~;'>“ ‘. 9. +1[@a§“%m(;§“'t>.] =(\§\.§ (

(\~\‘)':i + 2Y\1\;“)+(“1_“)§5\) + u‘\;‘*‘> ms

(x+ 2.\v\5 1: O

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cum ‘“*“- 3 +(1.v\+1.\1‘““

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 11: Chap02 Solutions Ex 2 4 Calculus

N) (5) )u=.~»-u , gm = -‘-1-gm = -4-1~<>=<= => §°‘(.,)

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Exercise 2.4 of Calculus and Analytical Geometry

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Page 12: Chap02 Solutions Ex 2 4 Calculus

"- '7 .Y "' 8511 (aarc sin x). prove that

U _)e).y(~+z) _ (2"+ 1) ’y(~+n__ (n1__az).y1»)

Sol. 3 1bk“. b.).J\.‘\. wk

5 = ‘<1->(s-.:.‘n.=‘¥J_-_=\1\-

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\ (\-13); =ZC»‘(s.-.2‘vO

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(‘§)(\-11)+~n(~; ) (-1.1).\.*g_L_§.2.).L,;|)(_t)__{(\j).1\.\.-v\(~§) . |) =_A§

U"*‘) KM-\)0- “ k

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x “'3 +U-x 3%‘ "‘ (1-Y\\'\)*§“ Q - (“‘_&) Q“ = O

1. If _v - ¢'1@'"_*"* show_thIt

<1-»’»> y‘""’ -<1»+%1> >w"Y“’—(»’+m’) W’. " 0-

Find lhc value of )7’ at x = 0

Mr.‘Silh 5 = a 1

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Exercise 2.4 of Calculus and Analytical Geometry

Page 12 of 20 Available at www.mathcity.org

Page 13: Chap02 Solutions Ex 2 4 Calculus

1 -I\'w'n‘J~‘i wv\= €_ ' -_—-‘-

B §\-1‘-vawii

7 Ya

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u-m-1§~>"~(-*\*3L = “K1557 /A am. .1;-J.v> 1") 15

u-mi’ -*5 = “*5 _----C1‘)mg. w-1\.i:-x ~n‘\'l'-~J>

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u-ma -wv) -L»-*3‘) -*3 - -\ v~»\ L“)

(\_,':~)$;')__(;_“.\,\)y\&5 )_(y1“-Y\-\-v\-v&)‘j = 0

um. mm (‘W ‘

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%MZ¢§ ’=(~%~~3r~3§)(<>)

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Exercise 2.4 of Calculus and Analytical Geometry

Page 13 of 20 Available at www.mathcity.org

Page 14: Chap02 Solutions Ex 2 4 Calculus

F0’\.Y\:'.\ , t;)(o) : (\l-\-vv‘\')§ (0) : (\L-\'Y\})-‘rV\

Fun-I 2 gnu) = (IL-\-Yzx); U’) = (2-L""\"})w:-

Fm “=3 5 l§)(o) = L;-'<Y}\>\;)(“) = (f;“+vv:‘)(\L+vu‘>.vv\

CI

p...»~=~ .‘§’n@> = <~m:>§"¢»s = <*~‘-~»&)(i*~-k>‘-?

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on W-1 -}"°"4

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»"~\+- ~-~*~ *wax;-> 117*

I \ .(\+-3'-"'z§u -Wm:-;~> F»?

W ,\=(, , £3)“; = (g§..&)‘§’g-3 = (c-.‘».-‘x)W‘+»&“3l1‘+w%).w\~"

1. ;_)L\l. “AM 5‘, Y\ OM.j“(,,§ .['(\.\§'~vv~} - -- - (3~w\ -\-w

,; ,1‘ 1;;

Exercise 2.4 of Calculus and Analytical Geometry

Page 14 of 20 Available at www.mathcity.org

Page 15: Chap02 Solutions Ex 2 4 Calculus

s = 31-==-»~ --‘<9\a-1'"

IE?)-\L\+¢>5‘= \

"' '1 : Q(\+1‘).v;3 -""3U-\-*l">j" +5“), = O

;‘~“_g_,_;.,h,.‘c-7L W\J(-\'¢w\-IJ

l “*3 K3&3'(\+\"*)’) -\-XQ1)“ = O

\ cl‘ . ) 1“

um BA) UH) "bis Q um-1.\ ym ,k‘~-‘)(‘J)(\~w)~~<\L_5') .(=»>+”l£‘1‘:§-Ala) -in +(v)-‘>\-“(\1) -I =

‘Qq gvm) ' ' 0.9 \\-M) W)(\+-:o~)_\j 4.1_~n~A\) 4, L~4(‘_w\\ j + Xj _\. wuj = 0

k * \(\-nf‘) ‘K I +(1v\+\§1\5““) 4, Ln‘-v\+m§ \§“3 = 0

(,\+»\‘33§*')+<_z~\+\)»\§“*“+ 'v\L\_‘\§‘) = ° --—-— @PA: 1:0 @@,@¢@

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F-w~.-=1 ,3(») :..(1).)(Q) = _(_z)-0-.:o=)\5 (0) = O

D (5) 1(1) 1. 1 1(|.)\-\Fit “=3 , gm») =-(-9.j(.,3 = -(3)--0) =) 3 (O) = (_\§'.;‘_ 31

(O 1 \"\ .1(3)

v.~~?~=-. \3(~=\ = -<~<>.3’<~>= _(~.§.<> =0 => 3 (.1): O

‘ ‘ m 1 \;) ,_ t 103+! 3

Fl“:-L) .§';)(°\ = -—l_(~$L-§‘§)‘.°> = -(5)30 :0 @ §(“)(o) = O

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5 (~=)= (-0,.\‘.1>-5-------km-\>kw)5 (Q) 1: Q

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Exercise 2.4 of Calculus and Analytical Geometry

Page 15 of 20 Available at www.mathcity.org

Page 16: Chap02 Solutions Ex 2 4 Calculus

4;Sol. 0») y -(X+\11*; )"

/5 _. \vv\k1\-\-h+‘L3“-‘. (M. ‘Fax xx)

= vv~(1+jT,'{=) .(1+ T:_\.:___;‘)

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= Yv\(‘A&-I\:~I\)_ .§~A~j'\TF)--L-—-—

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(Hi Owl) (M-\))j +Q2.Y\+\)‘l.‘) -\'(~r}-v~k)(5\) = o '

Exercise 2.4 of Calculus and Analytical Geometry

Page 16 of 20 Available at www.mathcity.org

Page 17: Chap02 Solutions Ex 2 4 Calculus

P~k>\==ob-®,®>@' “' i

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Exercise 2.4 of Calculus and Analytical Geometry

Page 17 of 20 Available at www.mathcity.org

Page 18: Chap02 Solutions Ex 2 4 Calculus

Z §\_,* = "\ +:§\-Kv.

' 2~A§\..u§'(_13= -\-\-.Y\:Ib'-Q},-u-A-‘K-‘L .~

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*-u(\~\)§"(1) .» z.§'(u\(-n+1) -H = 0

M1 (\-xx) §"(u\ + 2 (1-‘£n\§§’(~A3 -H = 0

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Exercise 2.4 of Calculus and Analytical Geometry

Page 18 of 20 Available at www.mathcity.org

Page 19: Chap02 Solutions Ex 2 4 Calculus

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Exercise 2.4 of Calculus and Analytical Geometry

Page 19 of 20 Available at www.mathcity.org

Page 20: Chap02 Solutions Ex 2 4 Calculus

-_ - -\. - . -K ] _ “(“ \)\_ ("\3.v\(_“-\)(‘-1-)’.i (_\)1“(“_\)(“_\)l“-‘IX 1 ‘ ‘

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Exercise 2.4 of Calculus and Analytical Geometry

Page 20 of 20 Available at www.mathcity.org