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Consider an elliptic paraboloid
f (x, y) = 4 - x2 - y2/4.
a. Find the xy-, yz- and xz-traces of the graph of f(x, y) and sketch the graph.
b. Write down the equation of the level curve which passes through a point (2.4). Sketch the level curve.
c. Find the unit vectors in the directions of the steepest descent and the steepest ascent at (2, 4). Mark these directions on the graph in (b).
d. Verify that the gradient at (2, 4) is orthogonal to the level curve through this point.
(e) Write down the equation of the tangent line to the level curve at (2, 4).
find the centroid of a thin, flat plate covering the region enclosed by the parabola y^2=x and the line x=2y.
a card drawn from a standard deck of playing cards. a)what is probability that it is an ace? b)what is probability tu be a face card.
The bus driver said, "We have gone 33 miles so far. If we continue to travel at the same rate, how many more minutes until we arrive?"
1. in a study of fraternal twins of different genders researchers measured the heights of each twin. the data show that
The volume of a sphere of radius R is v(R)=4piR^3/3. If the radius is increased by delta(r), what is the increase in volume to the first order? Type in your answer using D in place of delta(r).
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Composition of Functions and Isomorphisms, I can't prove the following statements about functions f:A->B and g:B->C, 1. If gof is one-to-one then so is f.
Find the slope of the line shown and interpret the slope as a rate of change given the following information. I am supposed to present this in business terms using Exxon Mobile as the example and using the mathematical concept of slope and rate of..
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