i need help finding the linear approximation of f(x,y)=x^2/(y^2+1)
local linear approximation?
Linear approximation usually involve a given point. Please write in question word for word as given.
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).
you there?
had to fix a sammich.
are you able to help me solve this?
just hold tight a sec.
k
\[L(x,y)=f (x _{0},y _{0})+f _{x}(x _{0},y _{0})(x -x _{0})+f _{y}(x _{0},y _{0})(y -y _{0})\]
and once i plug in those values.. that would be my answer?
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.
ok makes sense... but the answer is asking for a decimal answer... it wont take the whole thing.
any suggestions for this?
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
o ok i see what they are saying.. i will try this again and keep my fingers crossed. thank you.
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