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The length of a rectangle is six less than twice x; the width is two more than the product of four and x.
1. Write an expression which represents the length of the rectangle in terms of x.
2. Write an expression which represents the width of the rectangle in terms of x
3. Write an equation which represents the perimeter of the rectangle in terms of x and simplify.
4. Based on your answer to part c, are polynomials closed under the operation addition? Explain why or why not
5. Write an expression which represents the area of the rectangle in terms of x and simplify.
6. Based on your answer to part e, are polynomials closed under the operation multiplication? Explain why or why not
Why is dy/dx = (dy/du)(du/dx) an insufficient proof of the Chain Rule? In almost all Calculus textbooks, dy/dx = (dy/du)(du/dx) is given as a good rationale for the Chain Rule.
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