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Mathematics 19 Online
OpenStudy (anonymous):

Clac 3 Linearization: Find the Linearization of the function f(x,y,z)=sqrt(2x^2+3y^2+z^2) at (2,3,3). My work: I found that f(2,3,3)=sqrt(44) df/dx=8+(1/(2sqrt(44))) df/dy=18+(1/(2sqrt(44))) df/dx=6+(1/(2sqrt(44))) so the linearization=sqrt(44)+((8+(1/(2sqrt(44))))(x-2))+((18+(1/(2sqrt(44))))(y-3))+((6+(1/(2sqrt(44))))(z-3)). I am being told that this is incorrect and was trying to figure out why

OpenStudy (anonymous):

\[(x,y,z)= \sqrt{(2x^2+3y^2+z^2)}\,\,\,\,\,at (2,3,3).\] Hey linearization is a linear function in all the three variables. What is ur soln ?

OpenStudy (anonymous):

are you saying that sqrt(44)+((8+(1/(2sqrt(44))))(x-2))+((18+(1/(2sqrt(44))))(y-3))+((6+(1/(2sqrt(44))))(z-3)) needs to be simplified more?

OpenStudy (anonymous):

I am saying the linearization is not a number neither three numbers it is a linear \[\color{red}{\frak{Function}}\]

OpenStudy (anonymous):

humm ok so what should i be looking for?

OpenStudy (anonymous):

the numbers 8, 18,, 6 are \[\color{yellow}{MULTIPLIERS,\,\,\,NOT\,\,\,\,SUMMANDS}\]

OpenStudy (anonymous):

THEY ARE 3 "SLOPES", so to say

OpenStudy (anonymous):

instead of "+" it should be "*" after each of them, meaning multiplication

OpenStudy (anonymous):

after each of what? the 8,16,6?

OpenStudy (anonymous):

\[ df/dx=8(1/(2sqrt(44)))\]

OpenStudy (anonymous):

got it lol for some reason i was thinging +'s

OpenStudy (anonymous):

just realized what was going on. Tyvm lol

OpenStudy (anonymous):

what is tyvm ?

OpenStudy (anonymous):

thank you very much

OpenStudy (anonymous):

thx 4 xplnshn

OpenStudy (anonymous):

for some reason i thinking chain rule added the parts together

OpenStudy (anonymous):

It is rather \[ \Huge CENTRAL\quad that\\ \Huge \,\,\, MULTIPLICATION\]

OpenStudy (anonymous):

What is the level and "year" you are studying this material in ?

OpenStudy (anonymous):

@BenBlackburn ?

OpenStudy (anonymous):

sophmore 2nd in college. its just been awhile. over the summer i took linear algebra and we did not do much of this stuff in clac 2. so some of this stuff is causing me to go back and refresh my memory

OpenStudy (anonymous):

so some careless errors are popping up

OpenStudy (anonymous):

Well the lecturer should have stressed 200 times the chain rule

OpenStudy (anonymous):

it is in fact deeply intertwined with the idea of LINEARIZATION look suppose y = K*x and z = M*y ===> obviously z = K*M*x

OpenStudy (anonymous):

the same with derivatives !

OpenStudy (anonymous):

Well good luck & farewell.

OpenStudy (anonymous):

haha ty you too

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