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(a) Derive the analogs of Formulas (12) and (13) for surfaces of the form
(b) Let
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Calculus: Early Transcendentals, Enhanced Etext
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- Consider the function f(x, y) = (eª − x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (4, 2) in the direction in which f decreases most rapidly. vector = (b) Suppose v = 77 +73+ ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 2). What is a? a =arrow_forwardSketch the surface z = 3x? + y? + 1 and find its linear approximation at P-(0,-1)arrow_forwardState how the direction of gradφ relates to surfaces of constant φ(x, y, z).arrow_forward
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