Ask your own question, for FREE!
Mathematics 8 Online
OpenStudy (anonymous):

Consider a function f(x,y) = sqrt(20-x2-7y2). Using linear approximation of f near (2,1), find how large the approximated value of f(1.95, 1.08) is from the exact value a) 0.44% b) 0.28% c) 0.33% d) 0.55% e) None of the above

OpenStudy (amistre64):

using linear approximation eh .... gonna have to define a tangent plane maybe?

OpenStudy (amistre64):

unless you have some other methods in mind

OpenStudy (amistre64):

\[f(x,y,z)=(20-x^2-7y^2)^{1/2}-z\] \[f_x=-x(20-x^2-7y^2)^{-1/2}\] \[f_x=-7y(20-x^2-7y^2)^{-1/2}\] \[f_z=-1\] these partials give us the equations for the normal to the plane defined by using the given x,y point values \[f_x=-2(20-2^2-7)^{-1/2}=-2/3\]\[f_x=-7/3\]\[f_z=-1\] N=<2,7,3> and using the point (2,1,3) as the anchor gives us the tangent plane as: 2(x-2)+7(y-1)+3(z-3)=0

OpenStudy (amistre64):

now inputting the (1.95, 1.08) and solving for z gives us a value to compare with, so z=2.84667 by comparison is there a way that we can evaluate

OpenStudy (anonymous):

Thanks very much for your assistance but please how did you get the 2,7,3

OpenStudy (amistre64):

the gradient of an equation is a set of its partial derivatives. Those partial derivates define equations that relate to a parametric setup for the normal of a surface. By using the point given (2,1) i was able to establish the normal of the tangent plane at the given point

OpenStudy (amistre64):

since the normal is a vector, and vectors can be scaled, i scaled the partial results by a factor of -3 -3(-2/3) = 2 -3(-7/3) = 7 -3(-1) = 3

OpenStudy (anonymous):

ok

OpenStudy (amistre64):

im not sure how to determine the % accuracy without using a calculator to determine the value of f(1.95,1.08) to begin with, and im not sure if you knew of a method i might be forgetting

OpenStudy (anonymous):

I don't know of any method but am still working on it. Thanks very much for the assistance

OpenStudy (anonymous):

great....why did you divide it??

OpenStudy (amistre64):

suppose you have 2 number, p and q, and you want to know how much of a percentage difference there is between them. first get the value of the difference: p-q and divide that by the number you are wanting to find the percentage by p-q is what percentage of p? (p-q)/p

OpenStudy (amistre64):

prolly miss worded that one all over the place :)

OpenStudy (amistre64):

|dw:1363095775287:dw|

OpenStudy (anonymous):

Great, the answer showed negative, is it allowed to take it positive???

OpenStudy (amistre64):

positive is fine

OpenStudy (anonymous):

ok. Thanks very much! am very greatful for this help. God bless you

OpenStudy (amistre64):

youre welcome, i hope it made sense :)

OpenStudy (anonymous):

Find the maximum and minimum values of the function f(x,y) = xy subject to the constraint x2/2 + y2/2 = 1. Give the maximum and minimum values and the points at which they are attained. please can you help with this one??

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
laylasnii13: Can i dm anybody to vent having a rough time ??
13 hours ago 1 Reply 0 Medals
kaelynw: starting to draw a hand
4 hours ago 16 Replies 2 Medals
Twaylor: Rate it :D (Took 2 days)
13 hours ago 7 Replies 0 Medals
XShawtyX: Art, Short Writing Assignment: Imagining Landscapes
13 hours ago 4 Replies 1 Medal
XShawtyX: Chemistry, Help ud83dude4fud83cudffe
1 day ago 13 Replies 1 Medal
kaelynw: tried a lil smt, the arm is off but i like the other stuff
1 day ago 27 Replies 3 Medals
kaelynw: art igg
1 day ago 14 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!