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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, but they always say that a more rigorous proof is needed, since du can't equal 0. But du isn't 0, is it? It approaches 0, and both du's should approach 0 at the same "rate," since they're the same quantity. What's the problem with canceling them, then? Is it just because it doesn't use the definition of the derivative (with the epsilon-delta definition of a limit)?
A 6.00 in radius cylindrical rod is 2 ft long. Use a differential to approximate how much nickel (in in^3) is needed to coat the entire rod with the thickness of .12 in.
What is the least amount of wrapping paper that is needed to wrap a gift box that is 2 feet by 1 foot by 3 feet?
an inverted cone of revolution whose slant height is 15 cm. holds a liter of liquid. how far from the vertex should marks be placed on the slant height to indicate 1 milliliter?
Explain the importance of appropriately integrating Texas Instruments' CBL 2 (Calculator Based Laboratory), CBR 2 (Calculator Based Ranger), Fathom, a powerful data analysis software tool from Key Curriculum Press, and Excel into the middle school..
What are the co-ordinates of the point of intersection of lines M and N? Write the co-ordinates of the intersections of lines M and N with the x-axis. Write the co-ordinates of the intersection of lines M and N with the y-axis.
a piano has 88 keys.a piano repair shop has 4 broken pianos in its shop, some with key missing, how many pianos keys are in the shop?
Write an equation for a function that has a graph with the given transformations. the shape y=x2 is vertically strecthed by a factor of 10, and the resulting graph is reflected across the x-axis.
Consider second-price sealed bid auction. We assume that seller's value of the item is 0. There are three buyers whose private valuations θi are distributed uniformly on [0, 1]. All buyers simultaneously submit sealed bids bi ≥ 0. The buyer with the ..
The upper left-hand corner of a piece of paper 8 in. wide by 12 in. long is folded over to the righthand edge as in the figure. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y?
How much would a brand manager in Los Angeles have to make in order to have a higher salary than 99% of the brand managers in Houston?
You invested $10,000 in two bank accounts paying 8% and 10% annual interest, respectively. At the end of the year, the total interest from these investments was $940
The result is then folded in the obvious fashion. (If it isn't obvious, order one with sausage and pepperoni and invite you TA and UA to investigate.) How does one obtain the box of largest volume?
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