1. (a) What is related rates problems? Write down the necessity of related rates problems in calculus. Let A be the area of a square whose sides have length x and assume that x varies with time t. (i) Draw a picture of the square with the levels A and x placed appropriately. (ii) Write down an equation that relates A and x. (iii) Use the equation in part (ii) to find an equation that relates dA/dt and dx/dt. (iv) At a certain instant the sides are 3 ft long and increasing at a rate of 2 ft/min. How fast is the area increasing at that instant?

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