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LARLALUI 2.5.021. MY Consider the following. x2 + y2 - 81 (a) Find two explicit functions...
Question 1. Consider these real-valued functions of two variables: T In (x2 + y2) (a) () What is the maximal domain, D, for the functions f and g? Write D in set notation. (ii) What is the range of f and g? Is either function onto? ii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: z00, 2, 04 (Note: Use set notation, and draw a single contour diagram.) (v) Without finding...
Solve the given equation. Find y as an explicit function of x, if possible 2y' y2-1 = x Solve the given equation. Find y as an explicit function of x, if possible y+xe x y' = X
Problem 81 Find the point farthest from (1,3,-1) such that x2 + y2 + z2-11 and x-y+z < 3. What happens to the maximum distance if the 11 on the right side of the inequality is perturbed? 81. Suggestions (a) Take as objective the square of the distance from (x, y, z) to the point given (b) For the case of points inside the given sphere and with x-y+ z = 3, you might solve the Lagrange equations for x,...
Let MM be the capped cylindrical surface which is the union of
two surfaces, a cylinder given by x2+y2=81, 0≤z≤1x2+y2=81, 0≤z≤1,
and a hemispherical cap defined by x2+y2+(z−1)2=81,
z≥1x2+y2+(z−1)2=81, z≥1. For the vector field F=(zx+z2y+4y,
z3yx+4x, z4x2)F=(zx+z2y+4y, z3yx+4x, z4x2), compute
∬M(∇×F)⋅dS∬M(∇×F)⋅dS in any way you like
(1 point) Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by X2 + y2-81, 0 < ž < 1, and a hemispherical cap defined by...
(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 16 given the plane. x = k Find the trace. Identify the trace. circleellipse hyperbolaparabola y = k Find the trace. Identify the trace. circleellipse hyperbolaparabola z = k Find the trace. Identify the trace. circleellipse hyperbolaparabola Describe the surface from one of the graphs in the table. ellipsoidelliptic paraboloid hyperbolic paraboloidconehyperboloid of one sheethyperboloid of two sheets (b) If we change the equation in part (a) to...
1. (a) Write the following two functions in terms of , and say where they are holomorphic: i. x2 + y2 - y - 2+ ix ii. (x + 7txt) +i(y-2) (b) Show that the function f(x) = eri-y (cos(2«ry)+isin(2xy)) is entire, and find its deriva- tive. Write it in terms of .
PLEASE WRITE NEATLY.
Given the following two utility functions (the superscripts on the utility functions merely denote which utility function we are talking about): U" (x, y)-V x2 + y2 Demonstrate that the MRSxy is the same for the two utility functions U (x)y and
3. Consider the following system of equations (a) Check if the explicit functions, y,-hi (ri,T2) and y-h2(zi,T2), exist. (b) Find explicit functions. (c) Find and 2 h21, 2), exist all.
3. Consider the following system of equations (a) Check if the explicit functions, y,-hi (ri,T2) and y-h2(zi,T2), exist. (b) Find explicit functions. (c) Find and 2 h21, 2), exist all.
Verify that the given functions Y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. x2y" – 3xy' + 4y = 7x? In x, x>0; 71(x) = x2, yz(x) = x2 In x Y(x) =
11. [-/1 Points] DETAILS MY NOTES Find the volume of the region between the graph of f(x, y) = 81 – x2 - y2 and the xy plane. Submit Answer 12. [-/1 Points] DETAILS MY NOTES Find the volume of an ice cream cone bounded by the hemisphere z = V 50 - x2 y2 and the cone z = V + y2.