{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Math1 - Math 262 Fall 2009 Dec 18 ‘09 9:00 ~12200noon 1...

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Math 262 Fall 2009 Dec 18, ‘09, 9:00 ~12200noon 1) Determine the center, radius and interval of convergence (including end points) of ” (2x+5)"' a 3 ' _ n (egg—F2 “)3, (b) 2» .(2x 3) .1 _ 2 2) Evaluate Ixze" dx (1ermrl<.001). 0 , 3) Find the curvature of the twisted cubic r(t) = ti + tzj + ﬁt at a general point and at (0, 0, 0). Find also To), N0), 130:). 4) Let L(X, y) denote the local linear approximation to f(x, y) = «fxz + y2 at point (3, 4). Compute L(3'.01, 3.98). Give the second degree approximation PZ(x, y) 7' for f(x,y):\fx2+y2. . _ '5) Show that the equations ' xey +uz—cosv: 2 ucoservad—yz2 =1 can be solved for u and v as functions of x, y, 2 near point P0 where (x,y,z) = (2,0,1) and (u,v) = (1,0). Find also (6%2) at (x,y,z) é (2,0,1). My 6) Find and classify the critical points of f (x, y) = , 2 2 . 1 - x + y + x + y 7) Find the maximum and minimum values of for, y, z): xyz on the sphere x2+y27+zz=12 8) If z=f(x,y), where x=s+tand y=s—t-,_show-that (9212 _ a: 2 , @212 6x 8y as a: ' 9) Evaluate ”(336+ 4 y2 )giA, where; R is the region in the upper half—piane bounded R . ‘ . by the circles x2 +y2 =1 and 3:2 +3;2 =4_ ...
View Full Document

{[ snackBarMessage ]}