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Unformatted text preview: in the direction of most rapid increase at the point (0 , 1 , 2)? [3 pts.] 4. Derive the identity ( f v ) = f v + f v , (1) where f is a scalar eld and v is a vector eld. [5 pts.] 5. Evaluate the expression r , (2) where r is the position vector from the origin to the point r , using (i) Cartesian coordinates and (ii) spherical coordinates (cf. (6.32)). [3+2=5 pts.] 6. (a) Find the most general function f ( r ) of only the radial coordinate r =  r  such that ( f r ) = 0 except possibly at the origin r = 0. (b) Find the most general function g ( r,, ) such that ( g r ) = 0, again except possibly at the origin r = 0. [4+1=5 pts.] 7. Problems 10.1a,b,c,d. ( Curvature of a function ) [2+1+4+3=10 pts.] 8. Problem 10.1 g ( Stability of equilibrium ) [5 pts.]...
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 Fall '10
 Jacobson
 Physics

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