For both parts of this problem be sure you can

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For both parts of this problem, be sure you can explain what the practical meanings of the partial derivatives are.
A. z yy = z xx B. z yy = g ( x ) C. z yy = y D. z yy = 0
Correct Answers: D 8. (1 pt) If sin ( 1 x - 3 y + z ) = 0, use implicit differentiation to find the first partial derivatives z x and z y at the point (0, 0, 0). A. z x ( 0 , 0 , 0 ) = B. z y ( 0 , 0 , 0 ) = 1
Correct Answers: -1 3 9. (1 pt) The gas law for a fixed mass m of an ideal gas at absolute temperature T , pressure P , and volume V is PV = mRT , where 10. (1 pt) If z = cos y x , x = 4 t , y = 5 - t 2 , find dz / dt using the chain rule. Assume the variables are re- stricted to domains on which the functions are defined. 11. (1 pt) A bison is charging across the plain one morning. His path takes him to location ( x , y ) at time t , where x and y are functions of t , and north is in the direction of increasing y . The temperature is always colder farther north. As time passes, the sun rises in the sky, sending out more heat, and a cold front blows in from the east. At time t the air temperature H near the bison is given by H = f ( x , y , t ) . The chain rule expresses the derivative dH / dt as a sum of three terms:

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