HW4 solution

Section14534Dūflp1ک11wsof has maxi um rate of change along thegradient direction

ᶋ ᶆ҂/p҅ࡏ = 12x y.y DNi.DE6.9Rate of change 111 1116⊉ ݢ=Ӟ ࡎ ಷ P ˙ݗ

!2 4.4114

E ଚSince f so , f is increasing up in

the Ù direction

381 a p =ҁᤰ҅ᶆ҂1pইওஞ҅ک

Ӟ۹ ҂ hpӣ ҁ 3 1

1pH ԫஞ- 2 ྒ

b Rat of change

D嶍ಲӞ ⊉ · 11韷1111

C assume u is Vector as required

then rate of change along u is

鰯 f = 1111 11ᅩ11 cos 45

ԫ ݸ ҅ 1 ޙԫ ݸ

47 FCX.yzixztzxy.lyڊ (p = ҁڕ4̔#܄ 442ு

ԧ҅ নڝڝ bin

19 10 5

The tangent plane at p9 զ 2 110 y D 5෭ -1 0

qxtloy 5Z 33

section 146

6 ௪ ጬӾᬦy3ྲ - y)

2o 3ྲ2yᕁ҂ஞஞ

Ԇ-6cxzyinvwtI 6cut 2W 2 w vݞ

㊳ӣ3lxzyiczwt3cx-zyic-DWW- bcx-zgilw.MN)6 W_w 2 W_W hD

15 ӣ2 dwsuntl zplesiuwDzecxosln

ysiuwDE2eleUlwsusi.eulsinv 2

2e cos 2ˇ

ᝑᎣғ zioscz.nl…҂265 2

43 Let UEXctucx.tkflux.tlⰟ= flux.tn ڊ. ӣ fix ct) Cc)䆄 = fiux.tn.ྍ = fact ) ҁ1

咲+ cⶤ = fixctic-cstcfix.co)0

31 1ڹ eysmcnty 0

ělxltwscxzlxg Ѻԫ0xwscxzizyz.pe Xe

Zy1XWSLXZ