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This is the Exam of Multivariable which includes Interpret Mathematical, Integration, Region, Evaluate, Illustrate, Explanation Needed etc. Key important points are: Equal Difficulty, Continuous Partial, Function, Directional Derivative, Approximate, Function, Local Maximum, Local Minimum, Point, Saddle Points
Typology: Exams
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∇f (20, −100) = (5, −2),
and g(x, y) = f (xy^2 , 2 x^2 y). a. [6 points] What is ∇g(5, −2)?.
b. [6 points] Let n = (4, 2). What is the directional derivative dg dn
c. [6 points] Use the above to approximate g(4, 0).
x^2 + y^2 ≤ 36 , and x ≥ 0.
a. [7 points] What are the critical points of the height of the theatre?
b. [5 points] What is the maximum height of the theatre?
c. [5 points] What is the minimum height of the theatre?
a. [5 points] F : Rm^ → Rn^ is a function. If we can calculate the gradient of this function, what must be true about m and n?
b. [5 points] G : Rm^ → Rn^ is a function. If we can calculate the curl of this function, what must be true about m and n?
c. [5 points] H : Rm^ → Rn^ is a function. If we can calculate the the divergence of this function, what must be true about m and n?
ex^ y + 2 ey^ z − ez^ = 0.
a. [5 points] What is dz dx
b. [5 points] What is dx dy
c. [5 points] What is dy dz
d. [2 points] What is dz dx
dx dy
dy dz