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(12 poiuts) Let f(T,4,2) =Fyz Compute thc following:(a) FI(EV,2) =(6)-The direction of Lhe fastest tte of iucrease at the poiut (4,1.4)The nte of clnge of f in (hc ...

Question

(12 poiuts) Let f(T,4,2) =Fyz Compute thc following:(a) FI(EV,2) =(6)-The direction of Lhe fastest tte of iucrease at the poiut (4,1.4)The nte of clnge of f in (hc dlitrtion F (1,2cmi(Vf)=V * Vfpitts) Sckrt thtc corrcl acfiuitlon ft (u Fth c() to he flow ltna of tha vextur fickl F ou * with Initinl value c(O) (To Vo= (A) e() = F(c()) with c(o) (fo Uin 2u)(1) c() = F(c()) with c(0) (ro, {, #0)(C) *"() F(c(t)) with c() (ro; I,%

(12 poiuts) Let f(T,4,2) =Fyz Compute thc following: (a) FI(EV,2) = (6)-The direction of Lhe fastest tte of iucrease at the poiut (4,1.4) The nte of clnge of f in (hc dlitrtion F (1,2 cmi(Vf)=V * Vf pitts) Sckrt thtc corrcl acfiuitlon ft (u Fth c() to he flow ltna of tha vextur fickl F ou * with Initinl value c(O) (To Vo= (A) e() = F(c()) with c(o) (fo Uin 2u) (1) c() = F(c()) with c(0) (ro, {, #0) (C) *"() F(c(t)) with c() (ro; I,%



Answers

Find a unit vector in the direction in which $f$ increases most rapidly at $P,$ and find the rate of change of $f$ at $P$ in that direction. $$ f(x, y, z)=\frac{x}{z}+\frac{z}{y^{2}} ; \quad P(1,2,-2) $$

In discourse and win in the final, then turned up at first she called on the Lexx. I still watch it again. So is it for two? He expressed Jack scrip, huh? Less three. Why Swift? Jed? She Yes, Two x Cube. Jake. Less like you. This one. Okay, Now we need to find the doctor normal to the function that will be their gentle. That won't be the quantum security. Acceptable toe. One bicycle to one. And they're like, Oh, minus one. Make it. If I were not created now we have the vector normal. Put a person now will need to find a unit vector. You'd think I treaty you wondered why. Donna, please ls minus the sweat. I minus t. I don't know the sitter in indirect hunting, which the intelligence rapidly. Now we need to find out their sense were with a man. You're not Brendan Weapon point. She's 1/4 three square that's minus squid. Listen to find lunch

I have driven here it is given velocity field. We have to fight equations for streamline. Yeah. To the point Yeah. You want to come over coordinates. Mm off particle wow at please go to five seconds and please cut to second, hedge one comma But act discrepancy for a spin line. Mhm mm Be upon you scuttle. Do you buy upon topics? You is to find us? Do you accept on dating? Which is given so you uh and these to find us. Do you buy upon duty given A school to 155/s? We start to burn meter per second. Ex not escalate to one m. Why not one m. Do you notice Cal 20 be upon you is called to do you buy your panties be upon X separating the very big and integrating it for the given condition you will get equation to be What he's got to five none of X. But that's one right. No you is going to do you accept on duty this car to X. Separating aware of it. So the value of X. You will get it's not explanation of hair. Do you mind this? Do not? And we do you buy your on duty? It's got to be so do you buy his car too? Vdot integrating it. Uh huh. Yeah. From Equation three and 4. Why you can be written as why not be upon a runoff Except one x. much for particles. Mhm. At X. Not School to one. Why not is culpable at Please call 20. Yeah. Yeah. Actually X not. Uh huh. Here in two D minus. Do not can Britain it's Mhm. Act he's got over 1 2nd and why can return it's two m no. Okay at these cut to 12th X will be E. To the power to and why is for to live in veto and Y. X. You will rent that so thanks for watching it.

Hi everyone here it is given by the city feed we have to find lot of part lines for Please cut to 02 three seconds through a point. Mhm one Comotto act Please go to 0 2nd compared to straight lines. Mhm to the same point and and These cartoon three seconds velocity along excesses of the bar ticket. Do you accept on duty? It is given in the problem. XT separating the variable and integrating X. You will get here. He having the video will buy food our second square So you can write X to report to X. Not explanation of invite to do you square minus. Do you not escape? It's and on the bikes is it can be read in ads? No. Yeah. Do you worry upon duty which is given in the problem? Yeah, we hear one of me is given one by three meter per second separating the very well and integrating Yeah. Mm. Mhm by will be equal to buy. Not blessed. We even took T -3 months. So both lights are mm X is called two x. Not Explanation of a by two, please square minus. Do you notice where and vice, correct? Why not? Let's be into between my resting not Yeah. Yes. So strict lines are X straight. Yeah. When we X not explanation of a vitamin. Do you square minus? Do you know describe and why the split would be? Why not plus the Do you mind this too much? So if we brought the strict path, you will get X to be taken in meter. Why should we also take an emitter? Yeah, they're so thanks for Virginia.

Give it where the city field we have to fight it. Question for extreme like two point my lady. Mhm. Two comma five. Yes most of you. Mm Yeah coordinates of particle A. T. Score to two seconds. And that was At 04 edge. Mhm. Peace corps to do. Oh okay coordinates of apart ticket and Please cut to three seconds. Got parts. Mm hmm. Had please go to 1 2nd compare part lines. Extreme lights and street lights. Oh data given. Mhm. A scar to prove meter per second. 14 seconds. It's not it's multiple by not starting a fight. Yeah for streamline. Yeah be upon us curto do you buy upon dates? It is equal to Yeah we X upon a separating the very even and integrating it. No we will get by scott to buy a lot. Be upon two eggs access square minus X in this call substituting the given value. We will get wise cut to access four by four plus four. No velocity along X. Success after vertical stx upon duty. That is a Cross multiply it. And the access code to 80 integrating it. And subscribing the limit. You will get X. It's got two x not plus a. Do you mind necessity not? Okay velocity wrong by exist rely upon duty it's got to be X subject. Bring the value of X. Uh huh. Now integrating it and after simplifications you will get why is called to why not? Bless would be had not the minus T. Not Well as a bye to the Square -2 Notice Square. Uh huh. So to entry or depart lines. What? Mhm. Why particle? That was? Mhm. That it's not it's got 20 m. Why not? It's going to four metre egg judo at type Peace Corps to two seconds. You will get access for two for Peter and why is curto general meter at the time? to his cult? Oh, for particulate, That was aah mm. Yeah. Why is starting for five km? and he noticed for 2 1 2nd and at the scalp Three seconds we will get X is part of five m of ice for two. Hello Peter. So Paatelainen's. Yeah. Mhm mm. That's all. Thanks for watching it.


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