# sln10 - EAS4510 Homework#10 Solution#1 Given f x y = x 3 5...

This preview shows pages 1–2. Sign up to view the full content.

EAS4510 Homework #10 Solution #1) Given: 32 2 2 (, ) 5 8 2 5 0 31 0 8 0 22 0 fxy x x x y y f xx x f y y =+ ++−+ = =++ = =− = The only point that satisfies all three of these equations is: (, ) (2 , 1 ) xy The point (-1,1) also resembles a double point graphically but it does not satisfy all requirements. #2) ( ) cos f = (i) Taylor series approximation about 0 x : 00 () ( ) ( ) f xf x f x x x = +− Î 0 ( ) cos( ) sin( )( ) cos( ) sin( ) f xxx x x x δ (ii) Substite 0 x : 0 ( ) cos( ) cos( )cos( ) sin( )sin( ) f δδ = += Notice that these two results are very similar. Recall for small angles: cos( ) 1 sin( ) x x x Î 0 ( ) cos( ) cos( ) sin( ) f x = So we see that the two term Taylor approximation about 0 x is the same as a approximating ( ) cos f = as a small perturbation from the point 0 x . #3) a) 2 12 33 2 11 2 2 44 2 2 3( ) ) x x x y Ux x x x n x Uy y n y U yyy U yy µ ρρ µµ ρµ ρ µρ + + + ∂∂ ∂∂∂ 1 1 y y = 2 2 y y = 1 x x x + = 2 x x x ∂− = Î 1 2 1 2 5 5 2 2 1 2 2 21 2 5 5 1 2 ) ) 3 ( ) ( ) 3 ( ) ( ) x y U x x x x x x y y U x x x x y x ⎛⎞ = + + ⎜⎟ ⎝⎠ = + + Î

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/26/2008 for the course EAS 4510 taught by Professor Fitz-coy during the Spring '05 term at University of Florida.

### Page1 / 3

sln10 - EAS4510 Homework#10 Solution#1 Given f x y = x 3 5...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online