Calculus/Calculus

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Expert: Alon Mandes - 8/30/2009


Question
Concider the Function

f(x,y) = 1 + xy+x^2y^2

(a)Find the gradient vector of f(x, y) at the point (1,2).
(b)Find the directional derivative of f(x, y) at (1,2) in the direction of the vector v = i − 2j. Explain the meaning of your answer. At this point, in which direction should we move to make f(x, y) change most rapidly?


Answers
A) 10i+5j
B)  0  If B is equal to zero does this mean that it is a point on a tanget line  

Answer
B) The scalar product between the Gradient & the directional vector is zero , means that
the directional derivative is zero. that means it's a tangent plane. The direction to be
selected to obtain most rapidly changing in the function is always the path of the Gradient.

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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