Chapter 7a (Final KG, Exercise - 6)

DAO][BW — > J@EOI FN

Daoptbr —> J`eoi FN Bxbrd`sb -:

Oeswbr ? N`vbe8?. K`spiodblbet < 11==t 7. FN < :.7l 4. Icokbk (w) < 7==t (FN < ?.>l)

K`spiodblbet < 11==t

FN < :.7l

w < 7==t FN < ?.>l

FN cj vbssbi < :.7l FN cj icwbr acik <- 7.=l < ;.7l K↔ J`eoi K`spiodblbet (^) < K`spiodblbet cj vbssbi + dornc J`eoi K`spiodblbet (^) < 11==t + 7==t

J`eoi K`spiodblbet (^) < 0===t NN‐


NN‐

< 7== * ;.7 0===

NN‐↔

< =.=04l

@e`t`oi FN cj vbssbi NN‐↔  J`eoi FN cj vbssbi

< :.7l <-=.=04l < :.?=?l

J`eoi FN cj tab vbssbi `s :.?=?l

]onb ? cj ??

DAO][BW — > J@EOI FN

Oeswbr 7 N`vbe8?. K`sdaornbk (w) < :==t (FN < ??l) 7. FN cj vbssbi < :l 4. @e`t`oi K`spiodblbet < ?7:==t

FN < ??l

w < :==t

K`spiodblbet < ?7:==t

FN < :l

FN cj dornc FN cj vbssbi K↔

< ??l <-:l < 2l

J`eoi k`spiodblbet (^) < @e`t`oi k`spiodblbet — k`sdaornbk dornc J`eoi k`spiodblbet (^) < ?7:==t — :==t

J`eoi k`spiodblbet (^) < ?7===t NN‐


NN‐

< :== * 2 ?7===

NN‐

< =.72l

@e`t`oi FN NN‐ ↔  J`eoi FN

< :l <-=.72l < 2.>2l

J`eoi FN cj vbssbi `s 2.>2l

]onb 7 cj ??

DAO][BW — > J@EOI FN

Oeswbr 4 N`vbe8?. @e`t`oi K`spiodblbet < 00==t 7. FN < ;l 4. Icokbk (w) < ?==t (FN
FN < ?2l

w < ?==t

K`spiodblbet < 00==t

FN < ;l

FN cj dornc FN cj vbssbi K↟

< ?2l <-;l < ??l

@e`t`oi k`spiodblbet < 00==t Dornc icokbk <+?==t J`eoi k`spiodblbet(^) k`spiodblbet( ^) < ?====t NN‐


NN‐

< ?== * ?? ?====

NN‐

< =.??l

@e`t`oi FN NN‐ ↟  J`eoi FN

< ;.==l <+=.??l < ;.??l

J`eoi FN cj vbssbi `s ;.??l

]onb 4 cj ??

DAO][BW — > J@EOI FN

Oeswbr ; N`vbe8?. K`spiodblbet < ??2==t 7. FN < :.4l 4. K`sdaornbk (w) < 2==t (FN < 4 l)

K`spiodblbet < ??2==t

FN < :.4l

w < 2==t FN < 4l

FN cj vbssbi < :.4l FN cj icwbr acik <- 4.=l < 4.4l K↔ J`eoi K`spiodblbet (^) < K`spiodblbet cj vbssbi - dornc J`eoi K`spiodblbet (^) < ??2==t - 2==t

J`eoi K`spiodblbet (^) < ??===t NN‐


NN‐

< 2== * 4.4 ??===

NN‐↟

< =.?2l

@e`t`oi FN cj vbssbi NN‐↟  J`eoi FN cj vbssbi

< :.4l <+=.?2l < :.;2l

J`eoi FN cj tab vbssbi `s :.;2l

]onb ; cj ??

DAO][BW — > J@EOI FN

Oeswbr 2 N`vbe8?. Dornc sa`jtbk (w) <2==t 7. K < ?2l ↔ 4. K`spiodblbet (^) < ?====t

w < 2==t K`spiodblbet < ?====t K ↔ < ?2l

NN‐ < w * k ^ NN‐ < 2== * ?2 ?==== NN‐ < =.>2l↔

FN cj tab sa`p w`ii kbdrbosb gbdousb dornc aos gbbe sa`jtbk vbrt`doiiy kcweworks.

Oeswbr : N`vbe8?. 7. 4. ;. 2.

K`spiodblbet (^) < 0===t FN cj sa`p < ?=.2l Dornc sa`jtbk (w) < 4==t FN cj Icwbr Acik < 7.2l FN cj Rppbr Kbdf < ??.2l

w < 4==t K`spiodblbet < 0===t FN < ??.2l FN < ?=.2l FN < 7.2l

]onb 2 cj ??

DAO][BW — > J@EOI FN FN Rppbr Kbdf < ??.2l FN Icwbr Kbdf Kbdf < - 7.2l 7.2l K↟ < 0.=l NN‐

< w*k ^

NN‐

< 4== * 0 0===

NN‐ ↟ < =.4l

@e`t`oi FN cj vbssbi NN‐ ↟ J`eoi FN cj vbssbi

< ?=.2l < +=.4l < ?=.1l

J`eoi FN cj vbssbi `s ?=.1l

Oeswbr > N`vbe8?. 7. 4. ;.

K`spiodblbet (^) < 0==0t FN cj sa`p < 1.>l J`eoi FN rbqu`rbk < 0l FN cj Rppbr Kbdf < ?2l

w<3 K`spiodblbet < 0==0t FN < ?2l FN < 1.>l

Ibt dornc tc gb icokbk < w FN uppbr kbdf l K↟ < :.4l J`eoi FN rbqu`rbk FN cj vbssbi NN‐ ↟

< 0l <-1.>l < =.4l

NN‐ < w * k (^+w)

]onb : cj ??

DAO][BW — > J@EOI FN =.4 < w * :.4 0==0 + w =.4(0==0+w) < :.4w 7>=7.> + =.4w < :.4w 7>=7.> < :.4w — =.4w 7>=7.> < :w 7>=7.> < w :

;2=.;2t < w Dornc tc icok tc gr`en rbqu`rbk FN tc 0l `s ;2=.;2t

Oeswbr 1 N`vbe8?. 7. 4. ;. 2. :.

Abok cj kbrr`df < 7=l ogcvb fbbi ^b`nat cj icdclct`vb (w) < 4==t FN cj uppbr kbdf < 1l FN cj icwbr kbdf < 7l @e`t`oi k`spiodblbet (^) < ?7===t @e`t`oi FN cj tab vbssbi < >.:l

FN cj kbrr`df < 7=l

w < 4==t K`spiodblbet < ?7===t FN < 1l FN < >.:l FN < 7l

]onb > cj ??

DAO][BW — > J@EOI FN (o) FN cj kbrr`df FN cj icdclct`vb K↟

< 7=l < -1l < ?7l

NN‐ < w * k ^ NN‐ < 4== * ?7 ?7=== NN‐↟< =.4l

@e`t`oi FN cj tab vbssbi < >.:l <+=.4l NN‐ ↟  J`eoi FN cj tab vbssbi < >.0l (g) FN cj icdclct`vb FN cj icwbr acik K↔

< 1l <-7l < :l

NN‐ < w * k ^ NN‐ < 4== * : ?7=== NN‐↔< =.?2l

@e`t`oi FN cj tab vbssbi < >.:l <-=.?2l NN‐ ↔  J`eoi FN cj tab vbssbi <>.;2l o) FN cj tab vbssbi wabe kbrr`df aos tofbe tab wb`na cjj tab uppbr kbdf `s >.0l. g) FN cj tab vbssbi ojtbr sa`jt`en `e >.;2l

]onb 1 cj ??

DAO][BW — > J@EOI FN

Oeswbr 0 N`vbe8?. 7. 4. ;. 2.

K`spiodblbet (^) < ;02=t FN < 0.7l ^b`nat cj icok <2=t FN uppbr kbdf < 1l FN cj kbrr`df < 72l

FN cj kbrr`df < 72l

w < 2=t K`spiodblbet < ;02=t FN < 1l FN < 0.7l

o) FN cj kbrr`df FN cj sa`p K↟

< 72l <-0.7l < ?2.1l

NN‐


NN‐

< 2= * ?2.1 ;02= + 2=

NN‐

< 2= * ?2.1 2===

NN‐ ↟ < =.?21l

@e`t`oi Fn cj sa`p < 0.7l <+=.?21l NN‐ ↟  J`eoi FN cj sa`p < 0.421l

]onb 0 cj ??

DAO][BW — > J@EOI FN g) FN cj sa`p FN cj uppbr kbdf K ↔  NN‐


NN‐

< 2= * ?.7 ;02= + 2=

NN‐

< 2= * ?.7 2===

< 0.7l <-1.=
NN‐ ↟ < =.=?7l

@e`t`oi Fn cj sa`p < 0.7l <-=.=?7l NN‐ ↟  J`eoi FN cj sa`p < 0.?11l

o. FN cj tab sa`p wabe wb`nat `s aoen`en gy tab kbrr`df `s 0.421l g. FN cj tab sa`p ojtbr icok`en `s 0.?11l

Oeswbr ?= N`vbe8?. FN cj kbrr`df < 77l 7. ^b`nat k`sdaornbk (w) < 7=t (FN<2l) 4. @e`t`oi k`spiodblbet(^) < :===t (FN<1l)

FN cj kbrr`df < 77l

K`spiodblbet < :===t w < 7=t FN < 1l

FN < 2l

]onb ?= cj ??

DAO][BW — > J@EOI FN o) FN cj kbrr`df FN cj dornc K↟

< 77l < -2l < ?>l

NN‐


NN‐

< 7= * ?> :===

NN‐ ↟ < =.=2>l

@e`t`oi Fn cj sa`p < 1l NN‐ ↟  <+=.=2>l J`eoi FN cj sa`p < 1.=2>l

g) FN cj sa`p FN cj dornc K↔ NN‐


NN‐

< 7= * 4 :=== - 7=

NN‐

< 7= * 4 201=

< 1l <-2l < 4l

NN‐ ↟ < =.=?l

@e`t`oi Fn cj sa`p < 1.=l <+=.=?l NN‐ ↟  J`eoi FN cj sa`p < 1.=?l

o. FN cj tab sa`p wabe kbrr`df i`jts tab wb`nat `s 1.=2>l g. FN cj tab sa`p ojtbr k`sdaorn`en `s 1.=?l

]onb ?? cj ??