<Text-field style="Heading 1" layout="Heading 1">Your Name......................... Class time:.................</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Problem 1</Text-field>

T1: 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"Solve" the equation 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

T2: Find the gradient and the gradient field for the function f(x,y) = 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 + 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

T3: For the function 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