1. Find an equation of the tangent line to the curve y = x√x that is parallel to the line y =1 + 3x.
2. The gas law for an ideal gas at absolute temperature T (in degrees kelvin), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant (in units of L · atm/(mol · K)). Suppose that, at a certain instant, P = 10 atm and is decreasing at a rate of 0.5 atm/min and V = 20 L and is increasing at a rate of 0.2 L/min. Find the rate of change of T with respect to time at that instant if n = 10 mol. What are the units of this rate of change?