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Compute the indicated derivative using the chain rule. y = U , U = x - 5; - dy dx dy dx Use I'Hospital's rule to find the limit. lim x- - 2x + 1 X - -00 -8X - Find dy/dx, using implicit differentiation. 4x + 9y = xy ay dy Compare your answer with the result obtained by first solving for y as a function of x and then taking the derivative. dx Find the indicated derivative using implicit differentiation. 2x 2 - 12 = 1; dy dx dy dx Find the indicated derivative using implicit differentiation. p2 - pq = 9p-q; dp da apThe average price of a two-bedroom apartment in downtown New York City during the real estate boom from 1994 to 2004 can be approximated by p(t) = 0.330.1of million dollars (0 S t s 10), where t is time in years. (t = 0 represents 1994.)+ What was the average price of a two-bedroom apartment in downtown New York City in 2004? (Round your answers to two significant digits.) HINT [See Quick Example 14.] million dollars How fast was the price increasing? million dollars per year A few weeks into the deadly SARS (Severe Acute Respiratory Syndrome) epidemic in 2003, the number of cases was increasing by about 4% each day. T On April 1, 2003 there were 1,804 cases. Find an exponential model that predicts the number A(t) of people infected t days after April 1, 2003. A(t) = Use your model to estimate how fast the epidemic was spreading on April 9, 2003. (Round your answer to the nearest whole number of new cases per day.) HINT [See Example 2.] new cases per day The number of CDs per hour that Snappy Hardware can manufacture at its plant is given by P = X0.6,0.4 where x is the number of workers at the plant and y is the monthly budget (in dollars). Assume that P is constant, and compute - when x = 100 and y = 200,000. HINT [See Example 5.] dx ay = $ dx per worker Interpret the result. The monthly budget to maintain production at the fixed level P is decreasing by approximately $ per additional worker at an employment level of 100 workers and a monthly operating budget of $200,000. In other words, increasing the workforce by one worker will result in a savings of approximately $ per month