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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.
writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a
Proof for Absolute Convergence Very first notice that |a n | is either a n or it is - a n depending upon its sign. The meaning of this is that we can then say, 0 a n +
simplify the expression 3/5/64
a man buy car at rs.50 and sells it at gain of 14% find the sp
Cristiano Ronaldo runs 33.6 kilometres per hour. Usain Bolt set world record for running 100 m at 9.58 sec. Show me how to compare these two sportsmen. Step by step.
Find out the Taylor Series for f (x) = e x about x = 0. Solution In fact this is one of the easier Taylor Series that we'll be asked to calculate. To find out the Taylor
Generate G(1000,1/2) and find the largest clique you can. A clique is a complete sub graph, that is, a set of vertices each pair of which is connected by an edge.
A small airplane used 5and2over3 gallons of fuel to fly a 2 hour trip.how many gallons were used each hour
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
I have a 40 question assignment for this topic, will you be able to complete it?
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