Word Count : 445

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To identify the level curves of the given functions, let's go through each one step by step. ### (i) \( f(x, y) = \sqrt{x^2 + y^2} \) This is the distance function from the origin in the plane. For a given level \( c \), the level curve corresponds to points \( (x, y) \) where: \[ \sqrt{x^2 + y^2} = c \] Squaring both sides: \[ x^2 + y^2 = c^2 \] This is the equation of a circle with radius \( c \) centered at the origin. ______ ___ ___ ___ ____ ___ ________ _________.
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