Please show me the steps, for atleast one of them so i can see the process Find

Question

Please show me the steps, for atleast one of them so i can see the process

Find the domain and range and describe the level curves for the function f(x, y). f(x, y) = 1/7x^2 + 6y^2 Domain: all points in the xy-plane except (0, 0); range: real numbers > 0; level curves: ellipses 7x^2 + 6y^2 = c Domain: all points in the xy-plane; range: real numbers > 0; level curves: ellipses 7x^2 + 6y^2 = c Domain: all points in the xy-plane; range: all real numbers; level curves: ellipses 7x^2 + 6y^2 = c Domain: all points in the xy-plane except (0, 0); range: all real numbers; level curves: ellipses 7x^2 + 6y^2 = c f(x, y) = ln (10x + 3y) Domain: all points in the xy-plane satisfying 10x + 3y greater-than or equal to 0; range: all real numbers; level curves: lines 10x + 3y = c Domain: all points in the xy-plane satisfying 10x + 3y > 0; range: real numbers z greater-than or equal to 0; level curves: lines 10x + 3y = c Domain: all points in the xy-plane; range: all real numbers; level curves: lines 10x + 3y = c Domain: all points in the xy-plane satisfying 10x + 3y > 0; range: all real numbers; level curves: lines 10x + 3y = c f(x, y) = squareroot 16 middot x^2 middot y^2 Domain: all points in the xy-plane satisfying x^2 + y^2 = 16; range: real numbers 0 less-than or equal to z less-than or equal to 4; level curves: circles with centers at (0, 0) and radii r, 0

Explanation / Answer

1)since f(x,y) doesnt exist at (0,0) domin is all real numbers except(0,0)

since 7x^2+3y^2 > 0 range is all real numbers greater than 0

answer is (A)

2)since logarithmic doesnt exist for negative numbers, domain is 10x+3y > 0,

range is all real numbers

answer is (D)

3)since 16-x^2-y^2 > 0 ,domain is x^2+y^2<16

since 16 - x^2-y^2 <16, range is 0<=z<=4

answer is (C)

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