Q1) If gas in a cylinder is maintained at aconstant temperature T, the pressure P is related to the volume bya formula of the form
\(P=\frac{nRT}{V-nb}-\frac{an^2}{V^2}\)
(a) in which a, b, n, and R are constants. Find dP/dV.
(b) Now suppose temperature is not constant and that T, P, and Vare functions of time t. Find dP/dt.
(c) Describe in words the meanings of dP/dV anddP/dt.
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Q2) Let f be a function such that f has critical pointsat x=-1,1, and 2. Suppose f' has a critical point at 0 and 2.f''(x) > 0 on (0,infinity), also f'' is not defined at 2, andf''<0 for negative x. Lastly, suppose f(2)=0, but f also has onepositive and one negative critical value. Sketch a graph off.
(draw a graph)
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Q1) If gas in a cylinder is maintained at aconstant temperature T, the pressure P is related to the volume bya formula of the form
\(P=\frac{nRT}{V-nb}-\frac{an^2}{V^2}\)
(a) in which a, b, n, and R are constants. Find dP/dV.
(b) Now suppose temperature is not constant and that T, P, and Vare functions of time t. Find dP/dt.
(c) Describe in words the meanings of dP/dV anddP/dt.
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Q2) Let f be a function such that f has critical pointsat x=-1,1, and 2. Suppose f' has a critical point at 0 and 2.f''(x) > 0 on (0,infinity), also f'' is not defined at 2, andf''<0 for negative x. Lastly, suppose f(2)=0, but f also has onepositive and one negative critical value. Sketch a graph off.
(draw a graph)
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