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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.
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Regression line drawn as y=c+1075x, when x was 2, and y was 239, given that y intercept was 11. Caculate the residual
1. The polynomial G(x) = -0.006x4 + 0.140x3 - 0.53x2 + 1.79x measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase
The next special form of the line which we have to look at is the point-slope form of the line. This form is extremely useful for writing the equation of any line. If we know that
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The remainder when 5^99 is divided by 13 Ans) 8 is the remainder.
I need to follow the pattern .125,.25,.375,.5, ?
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If X = {a, e, i, o, u} and Y = {a, b, c, d, e}, then what is Y - X ?
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