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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.
4/(x+7)(x+4)
Indeterminate forms Limits we specified methods for dealing with the following limits. In the first limit if we plugged in x = 4 we would get 0/0 & in the second limit
how to do it
Owner of a computer repair shop has daily revenue with mean $7200 and SD $1200 Daily revenue for next 30 days will be monitored. What is probability that daily revenue for those 30
Provide the vector for each of the following. (a) The vector from (2, -7, 0) - (1, - 3, - 5 ) (b) The vector from (1,-3,-5) - (2, - 7, 0) (c) The position vector for ( -
Factorize x squared + 6x + 8
find the simple interest on Rs. 68,000 at 50/3 per annum for 9 month
how it solved
What are the marketing communications for Special K
Given a standard 2x3 matrix show the ideal formed by the 2x2 minors is Prime.
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