Describe in words the level surfaces of g(x, y, z) = e-(x²+(y-1)'+z²). Think what the intersections of these surfaces with the three coordinate planes look like. (a) In symbolic form, these level surfaces are given by e-(x²+(y-1)+z*) = c where c is a constant. For what values of c are level surfaces defined? CE (Give your answer as an interval or list of intervals; for example, if c is less than 1 or greater than or equal to 2, enter (-inf, 1),[2,inf).) (b) Pick a level surface that intersects the xz-plane. What is your value of c? Write the equation for the intersection, as an expression set equal to a constant: (c) Pick a level surface that intersects the yz-plane. What is your value of c (which might be different from that you used in (a)? C = Write the equation for the intersection, as an expression set equal to a constant: 0-0 (d) Pick a level surface that intersects the xy-plane. What is your value of c? c = Write the equation for the intersection, as an expression set equal to a constant: O-0

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