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@@ -812,7 +812,11 @@ j. **Concluding and Intuitive Explanations**
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- Conclude with an intuitive explanation of why the result makes sense, possibly connecting it to known theorems or simple examples.
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- In notes after the proof, highlight potential sources of confusion for students and clarify tricky aspects of the problem.
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10.
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11. When finding critical points in multivariable calculus:
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- Always check what happens when any variable equals zero (except where undefined)
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- Conclude with an intuitive explanation of why the result makes sense, possibly connecting it to known theorems or simple examples.
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- In notes after the proof, highlight potential sources of confusion for students and clarify tricky aspects of the problem.
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10. If you specify a quadrant restriction (e.g. "in the first quadrant")
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in a problem with calculating area between lines/curves or volume between surfaces,
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make sure the question is CLEAR about what regions you intend the solution.
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- NOT CLEAR example: "Find the area of the region bounded by the curves y = sin(x), y = cos(x), and x = 7*pi/4 in the first quadrant."
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- CLEAR example: "Find the area of the region bounded by the curves y = sin(x), y = cos(x), and x = 7*pi/4. Then find the area of that region that intersects with the first quadrant."
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11. When finding critical points in multivariable calculus:
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- Always check what happens when any variable equals zero (except where undefined)
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