In the following, remember that f(n)(x) represents the nth derivative of f, and assume s >...

Question:

In the following, remember that f(n)(x) represents the nth derivative of f, and assume s > 0.
(a) By giving an appropriately diverse selection of samples functions f, explain why it is reasonable to assume that for “most” functions f, there is some value s for which lim x→∞ f(x)e−sx = 0. (In other words, pretend you’re the teacher of a diﬀerential equations class trying to convince the class that this assumption is a reasonable one! Don’t just claim the limit is 0; show that the limit is 0 for your chosen example functions) (b) Suppose lim x→∞ f(x)e−sx = 0. Find lim x→∞ f(n)(x)e−sx. Suggestion: Visit the l’Hˆopital. (c) Suppose lim x→∞ f(n)(x)e−sx = 0. Find lim x→∞ f(x)e−sx. Suggestion: Your intuition should suggest it’s 0. What if it isn’t?

Similar Solved Questions

The loss L due to a boat accident is exponentially distributed. Boat insurance policy A covers...
The loss L due to a boat accident is exponentially distributed. Boat insurance policy A covers up to 1 unit for each loss. Boat insurance policy B covers up to 2 units for each loss. The probability that a loss is fully covered under policy B is 1.9 times the probability that it is fully covered und...
What is the ionic compound name for O_2?
What is the ionic compound name for O_2?...
A triangle has corners at (8 ,3 ), (4 ,-5 ), and (2 ,1 ). If the triangle is dilated by a factor of 5  about point (1 ,-3 ), how far will its centroid move?
A triangle has corners at (8 ,3 ), (4 ,-5 ), and (2 ,1 ). If the triangle is dilated by a factor of 5  about point (1 ,-3 ), how far will its centroid move?...