Question

i need help finding the linear approximation of f(x,y)=x^2/(y^2+1)

Answer 1

local linear approximation?

Answer 2

Linear approximation usually involve a given point. Please write in question word for word as given.

Answer 3

let f be defined as follows: f(x,y)=x^2/(y^2+1). use the linear approximation at an appropriate point (a,b) to estimate f(6.03,0.95).

Answer 4

you there?

Answer 5

had to fix a sammich.

Answer 6

are you able to help me solve this?

Answer 7

just hold tight a sec.

Answer 8

k

Answer 9

\[L(x,y)=f (x _{0},y _{0})+f _{x}(x _{0},y _{0})(x -x _{0})+f _{y}(x _{0},y _{0})(y -y _{0})\]

Answer 10

and once i plug in those values.. that would be my answer?

Answer 11

Yes. be careful, easy to make mistakes. Note partial derivative in respect to x, partial to y. In the case\[(x-x _{0})\]and y\[(y-y _{0})\]you keep the actual letter x and the letter y, where ever you see\[x _{0},y _{0}\]you plug in given x and y.

Answer 12

ok makes sense... but the answer is asking for a decimal answer... it wont take the whole thing.

Answer 13

any suggestions for this?

Answer 14

After re-reading question, they say an appropriate point (a,b). They want you to read between the lines and know the appropriate (a,b) is (6.00, 1.00). So above, where I say keep actual letter x and y, instead plug in x=6.00, y=1.00

Answer 15

o ok i see what they are saying.. i will try this again and keep my fingers crossed. thank you.