Functional Analysis Answers

It is the last question of my functional analysis assignment , I 've posted the question on stackexchage http://math.stackexchange.com/questions/181339/compactness-and-boundedness-of-integral-operator , but seems that no one there can help me on it . Thanks in advance for any help.

2:2

Martin expects to gain V kr for one of his company's products are described by the function
V (x) = 0.03 x ≦ 3 + 0.2 x where x is the number of units produced
a) Determine the marginal change in the settlements as output increases 100-101 units?
b) Find the marginal profit when it produces 110 units.

4:4

A company that manufactures thermos has developed a new thermos. By means of measurements have been studied its ability to maintain the temperature of the beverages. For coffee, it has been concluded that the following formula applies under certain conditions:

f (t) = 85 ∙ e r (t -0.038)

where f (t) is the temperature in ℃ and t is time in hours after coffee poured in.

a) Calculate the temperature of the coffee after 24 hours.
b) Formulate a question to be answered with the help of the solution to the equation
f (t) = 50
c) Solve the equation and answer your question.
d) What does the value f '(5) on the coffee?
e) Give one condition that must be satisfied for the formula to apply

If S,T Є B(X,X),show that for any λ Є ρ(S) intersection ρ(T),
Rλ(S) - Rλ(T) = Rλ(S) (T – S) Rλ(T)