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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.
what is 9/8
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Q. Adding Fractions with the Same Denominator? Adding fractions with the same denominator is easy- you add the numerators (the tops), and you leave the denominator alone!
Two Tailed Tests A two tailed test is generally used in statistical work as tests of significance for illustration, if a complaint lodged by the client is about a product not m
If a telephone pole weighs 11.5 pounds per foot, how much does a 32-foot pole weigh? Multiply 11.5 by 32; 11.5 × 32 = 368 pounds.
what are the factors af 34?
Well, my uncle want me to tutor him in mathematics. But, the problem is I don''t know what he already knows about math. It for his Compass Test when he go back to school in the spr
Can two lines contain a given point
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