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Let f : R3 → R be de?ned by: f(x, y, z) = xy2+ x3z4+ y5z6
a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) .
b) Brie?y explain why f must be a di?erentiable function (you just need to "look" at the equations for the partial derivatives).
c) Find D~uf(2, 1, 1) where ~u is a unit vector in the direction of ~v = h4, 3,-1i .
d) Find an equation for the plane which is tangent to the surface de?ned by
xy2+ x3z4+ y5z6= 11
at the point (2, 1, 1) .
e) Use di?erentials to approximate the value of f(2.01, 1.02, 0.97) . Use a calculator to?nd a more accurate value, and compare.
Identify the flaw in the following argument which supposedly determines that n 2 is even when n is an even integer. As well name the reasoning: Assume that n 2 is
Diagonals of a trapezium divide each other proportionally: Given : In trapezium ABCD , AB// DC R.T.P :AO/OC = BO/OD Construction: Draw the line PQ; parallel to AB or C
Computation method Whereas L = Lower class boundary of the class having the mode f 0 = Frequency of the class below the modal class
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What is Congruent Angles in Parallel Lines ? Postulate 4.1 (The Parallel Postulate) Through a given point not on a line there is exactly one line parallel to the line. T
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The law of cosines can only be applied to acute triangles. Is this true or false?
Rationalize the denominator for following. Suppose that x is positive. Solution We'll have to start this one off along with first using the third property of radica
Multiply following and write the answers in standard form. (a) 7 i ( -5 + 2 i ) (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu
Find out the roots of the subsequent pure quadratic equation: Find out the roots of the subsequent pure quadratic equation. 4x 2 - 100 = 0 Solution: Using Equation
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