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Consider F(x,y,z)= √(x + yz), P(3,1,1,) and u= (2/7, 6/7, 3/7)
a) Find the gradient of F.
b) Evaluate the gradient at point P.
c) Find the rate of change of f at P in the direction of the vector u.
d) Find an equation of the tangent plane to √(x + yz) = 2j at the point P(3,1,1).
Find the average value of f(x,y)=x2/3y1/3 over the rectangle R={(x,y)/-8≤x≤8,0≤y≤27}
the base of a solid is an ellipse whose major axis and minor axis are 12 and 8cm long, respectively. what is the volume of the solid if every section perpendicular to the major axis is an is an equilateral triangle.
The formula used to find the half-life of a substance is y = nekt, where y is the amount remaining, t is the amount of time in years, and n is the initial amount of the substance. Based on this information, what is the approximate value of k?
What is the area between a raw score of 113 and 126 in a normal distribution with a mean of 100 and a standard deviation of 10 ?
What are the odds against the series going a full seven games
Suppose p3 represents the proportion of patients who showed improvement after one month of therapy three times a week and p2 represents the proportion of patients who showed improvement after one month of therapy twice a week. A 95% confidence int..
Frank is going to buy some ties at $7.50 per tie and some shirts at $18.50 per shirt. If he buys twice as many ties as shirts and spends no more then $205, what is the greatest number of shirts he can buy?
The 4 runners on a relay team all want to run the same distance in a race. The coach says that the first runner will go 1/4 of the distance. Then the second runner will go 1/3 of the remaining distance
Using the definition of the derivative and any standard limiting theorems, show that the derivative of (sinx)^2 is sin(2x).
The upper right-hand corner of a piece of paper, 11 in. by 6 in., as in the figure, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y?
question a recreation room has the following dimension. carpeting will cost 9.00 a square yard. how many square yards
Linear Mappings, Differentiation and Linear Spaces, If l is a nonzero scalar linear function on linear space X (which may be finite or infinite) and a is an arbitrary scalar, there exists a vector x in X st l(x)=a
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