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Unformatted text preview: f = f Chain Rule for Partial Derivatives : Suppose z is a function of x and y, each of which is a function of t. Then z can be regarded as a function of t and Incremental Approximation Formula For Functions of Two Variables : Suppose z is a function of x and y. If x denotes a small change in x and y a small change in y, the corresponding change in z is Ex. 3 At a certain factory, the daily output is Q= 60KL units, where K denotes the capital investment measured in units of $1000 and L the size of the labor force measured in worker-hours. The current capital investment is $900,000, and 1,000 worker-hours of labor are used each day. Estimate the change in output that will result if capital investment is increased by $1,000 and labor in increased by 2 worker-hours. Solution: Apply the approximation formula with K = 900, L = 1,000, K = 1, and L = 2 to get, =30KLK+20KLL =30(1/30)(10)(1)+20(30)(1/100)(2) =22 units Output will increase by 22 units...
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