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Consider the function f(x,y,z) = (e^z)ln(x^2 + y^2)
a) Is there a vector r such that the directional derivative of f at (1,1,0) in the direction of r equals 1? If there is, find one such vector. If not, explain why not.
b) Is there a vector r such the directional derivative of f at (1,1,0) in the direction of r equals to -2? If there is, find one such vector. If not, explain why not.
Explain how you would conduct the survey. What are the ethical implications if the manufacturer of Brand A toothpaste asked you to survey only its employees?
Let V be the set of functions having the set of real numbers as domain whose graphs pass through the point:
A reconnaissance airplane leaves its airport on the east coast of the United States and flies in a direction 85 degree. Because of bad weather, it returns to another airport 230 km due north of its home base.
Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled.
Find the test statistics
Let V be a circle lying in S. Then there is a unique plane P in R^3 such that p / S = V ( / = intersection). Recall from analytuc geomerty that
Compute the estimate for the standard error of the difference between two proportions.
Use augmented matrices
Show that the functions x and x^2 are orthogonal in P5 with inner product defined by ( =sum from i=1 to n of p(xi)*q*(xi) ) where xi=(i-3)/2 for i=1,...,5.
A power Station and a factory are on opposite sides of a river 60m wide. A cable must be run from the power station to the factory. it costs $25 per meter to run a cable in the river and $20 per meter on land.
Suppose u(x, y) and v(x, y) are harmonic in a region under? Under what condition is the product u(x, y) . v(x, y) harmonic? In particular, when is (u^2)(x, y) harmonic?
A printer is making a poster that will have a TOTAL AREA of 200 square inches and will have 1 inch margins on both sides, a 2 inch margin on the top and a 1.5 inch margin on the bottom.
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