Steady states If a function f represents a system that varies in time, the existence of lim t → ∞ f ( t ) means that the system reaches a steady state (or equilibrium). For the following systems, determine whether a steady slate exists and give the steady -state value . 70. The population of a bacteria culture is given by p ( t ) 2500 t + 1 .
Steady states If a function f represents a system that varies in time, the existence of lim t → ∞ f ( t ) means that the system reaches a steady state (or equilibrium). For the following systems, determine whether a steady slate exists and give the steady -state value . 70. The population of a bacteria culture is given by p ( t ) 2500 t + 1 .
Solution Summary: The author explains the steady state of the function p(t)=2500t+1.
Steady statesIf a function f represents a system that varies in time, the existence of
lim
t
→
∞
f
(
t
)
means that the system reaches a steady state (or equilibrium). For the following systems, determine whether a steady slate exists and give the steady -state value.
70. The population of a bacteria culture is given by
p
(
t
)
2500
t
+
1
.
evaluate
(a) lim x→ x^2 - 36/x^2 + 5x - 6
(b) the demand curve of a firm is p= -10q + 5900 and its average cost is
A(q) = 2q^2 - 4q + 140 + 845/q. where q is the firm's output produced and sold.
1. derive an expression for the total revenue of the firm.
2. derive an expression for the firm's total profit function
3. derive an expression for the rate of change of profit function of the firm.
4. is the rate of change of profit increasing or decreasing when the firm's output level is q= 50?
5. determine the level of output for which the total profit of the firm is maximized
6. what is the firm's maximum profit
Option D: Lim t -> 0 f(t,0) = 1 but lim t -> 0 f(0,t) = -1
The efficiency of an internal combustion engine is given below, where v1/v2 is the ratio of the uncompressed gas to the compressed gas and c is a positive constant dependent on the engine design.
Efficiency (%) = 100[1 − 4/(v1/v2)c]
Find the limit of the efficiency as the compression ratio approaches infinity.
Chapter 2 Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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