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Question 1.
Find all critical points of f(x,y) = x3 + y2 − 6xy + 6x + 3y and determine whether each is a local max, local min, or saddle point.
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Question 2.
Find the extreme points of f(x,y,z) = x + z subject to the constraint x2 + 3y2 + z2 = 4.
Question 3.
Find the moving frame T,N,B for the path x(t) = h4cos(2t),3t,−4sin(2t)i.
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Question 4.
Consider the vector field F(x,y) = (y,−x).
(a) Sketch the vector field.
(b) Calculate div(F) and curl(F).
(c) which of the following paths qualify as flow lines for F:
1(t) = hsin(2t),cos(2t)i r2(t) = hcos(3t),sin(3t)i
3(t) = hsin(t) + cos(t),sin(t) − cos(t)i
Question 5.
(a) Find the arc length for x(t) = ht3,3t2,6ti on the interval −1 ≤ t ≤ 2
(b) Find the arc length of the path from t = 0 to t = 2.
This is a sample question.can you help me find a tutor because I need him to help me solve five math problems in one hour at noon tomo
ow (11.pm). California time. will need answers within 1 hou
Only need the general problem-solving steps, already answered. Write it on the paper and take a photo and send it to me by email
sample file given, will provide the actual questions at noon tomo
ow (11.pm). California time
Only need the general problem-solving steps, already answered. Write it on the paper and take a photo and send it to me by email