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Question: (a) The graph of f (x, y) = (y - x2)(y - 2x2) intersects the xy-plane z = 0 in two parabolas. In the xy-plane, draw the domains where f is negative, and where f is positive. Show that (0, 0) is the only stationary point, and that it is a saddle point.
(b) Suppose (h, k) ≠ (0, 0) is any direction vector. Let g(t) = f (th, tk) and show that g has a local minimum at t = 0, whatever the direction (h, k) may be. (Thus, although (0, 0) is a saddle point, the function has a local minimum at the origin in each direction through the origin.)
ACCELERATION OF A CAR The distance s (in feet) covered by a car t sec after starting from rest is given.
Kendall Corners Inc. recently reported net income of $3.1 million and depreciation of $500,000. What was its net cash flow? Assume it had no amortization expense.
Skateboard racecourse A course for a skateboard race con- sists of a 200-meter downhill run and a 150-meter level portion.
Draw an aggregate-demand / aggregate-supply diagram to show the short-run effect of this decision on the economy. Label the new levels of prices and real output. Explain in words why the aggregate quantity of output supplied changes.
The following two sentences were devised by the logician Saul Kripke. While not intrinsically paradoxical, they could be paradoxical under certain circumstances. Describe such circumstances.
why is it important to ensure that a population sample is unbiased? in your own words give an example in detail of how
find the perimeter of one of the smaller rectangles using systems of equations.
A bag contains two red marbles, four green ones, one lavender one, three yellows, and five orange marbles. How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
1. consider the function f de?ned bythe ?rst and second derivatives of f area determine the domain of f . write your
A rocket is launched straight up. At t seconds after being launched, its altitude is given by h = 4t^2 metres. The line of sight from you to the rocket makes an angle θ radians with the horizontal. Four seconds after launch, by how many radians per ..
Design two versions of the explanatory notes. The first version must be suitable for use by new employees who are unfamiliar with the organisation's processes and have never used standard templates or macros. The second version must be suitable fo..
Let's start by describing some of the major characteristics and challenges of the World Trade Organization by using Brazil and Norway as examples. Then, let's discuss what some of the main steps forward as well as roadblocks in the Doha Rounds?
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