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Material Type: Exam; Class: Calc III for Comput Sci; Subject: Mathematics; University: Georgia Institute of Technology-Main Campus; Term: Unknown 1989;
Typology: Exams
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Consider a vector x =
x y z
. Provide an algorithm to compute a vector orthogonal to x. The subroutine should work
for all the following vectors.
x =
(^) , x =
(^) , x =
(^) , x =
(^) , x =
(^) , x =
Let x 0 =
, x 1 =
, p =
Compute the minimum distance between p and the line passing x 0 and x 1. Compute the minimum distance point q , i.e., compute q such that q is on the line and || p − q || is minimum.
Compute
Let A = VDV −^1 , where V =
, and let^ D^ =
Compute the trace and determinant of A.
Let f ( x , y ) = x^4 + y^3 + 2 xy^2. Compute ∇ f and Hf. Compute the quadratic approximation to f ( x , y ) at ( x , y ) = ( 1 , 1 ). Compute the maximum and minimum curvature at ( x , y ) = ( 1 , 1 ).
Let F ( x , y ) =
3 x^3 sin( y^2 ) cos( xy )
. Compute the Jacobian J F.
Next exam will be on Mar. 7.