1. Consider the function z = f(r, y) = V16 – r² – 4y². (i) Find the domain and range of the function. (ii) Sketch the level curve for z = 0 and trace of the function for y = 0. (iii) Sketch the graph of the function. 2. Sketch the level surface of the function w = f(x, y, 2) = z – a² – y² + 2x + 1 at w = 3. dz 3. Given that z = f(u, v), where u = 2x cos y and v = r sin y. Find and dz Hence, show that )+(烏) 2 2 2 1 (dz 4. du dv

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