Find the domain and range, and sketch the space curve:
2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of f? (b) Sketch the level curves for 2-f(r,y) -0,-3,-2V2,-v5 (c) Sketch the cross sections of the surface in the r-2 plane and in the y-z plane (d) Find any z, y and z intercepts Use the above information to identify and sketch the surface. 2. Consider the surface -v 9-2r2-r : f(x, y) z (a) What is the domain and range of...
1. Consider the region bounded by x = y, y = 0, and y=v2 - X. Sketch the region, and find its area.
2. Find and sketch the domain of the function f(x,y) = V x2 – y + 2.
Question 2 Find the domain of the function: f(x,y)= Trova cination for v) - In(9-x-y) a. D={(x,y)|x+y > 9 b. D={(x,y)|35x+y<9} C. D={(x,y)|x+y23} d. D={(x,y)|3<x+y<9}
QUESTION 9 Find the domain and range and describe the level curves for the function f(x,y) y+10 1(x, y)s a.Domain: all points in the x-y plane excluding x O: range: all real numbers; level curves: parabolas y ex2-10 b. Domain all points in the xey plane; range: real numbersz 0: level curves: parabolas y- ex2- 10 Domain :all points in the x-y plane; range: all real numbors; levol curvos: parabolas y ex2-10 d. Domain all points in the x-y plane...
G-ly~2 _ cos(x + y2z)ļi + [xz2-2yz cos(x + y2z)| j + 12.ryz-v2 cos(x + y%)| k. (a) Which of these two fields (if any) are conservative on R? Give detailed (b) Find potential functions for the fields that are conservative. (c) Calculate the line integralsF - dr and / G dr where C is the arc of the reasoning 2 2 curve formed by the intersection of the plane 4 and the surface zy in the first octant, oriented...
1. Sketch the domain of the following functions. (6 Pts) 12+y2 a) f(1,7) (b) g(x, y) = x2 + y2 - 4
X-2 3 of 9 5.(12 pts) let f(x) = ******. Graph the function and use it to find lim f(x) and lim f(x). Does lim f(x) exist? Find domain and range of f(x). 2 that are to the line - 4x + y = 5.
For problems 8-12, use the graph of y=f(x) and the table for g(x) and g'(x) to compute the indicated derivatives. Write your final answer and only your final answer) in the space provided. Answers should be exact and fractions should be used where appropriate (do not use numbers in decimal form). 1 -4 -2 g(x) 2 5/2 3 14/5 &'(x) 7/5 1/2 1/4 -1/4 0 2 قيا 2 - 1 -2 - 1/2 4 0 5 6 8 1 6...
Question 1. Consider these real-valued functions of two variables TVIn (r2y2) f (x, y)- 9(r,)2 2+4 (a) (i) 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? iii) Show that f is not one-to-one. (iv) Find and sketch the level sets of g with heights: z0 0, 20 2, 204 (Note: Use set notation, and draw a single contour...