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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?

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Cove's Cakes is a local bakery. Price and cost information follows: $ 14.71 Price per cake...

Cove's Cakes is a local bakery. Price and cost information follows: $ 14.71 Price per cake Variable cost per cake Ingredients Direct labor Overhead (box, etc.) Fixed cost per month 2.28 1.10 0.14 $5,147.40 Required: 1. Determine Cove's break-even point in units and sales dollars. 2. Determin...

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Question : 1 Budgeted Sales April (Actual) S7200,000 May 8400,000 June 1 020,000 July 1.080,000 August...

Question : 1 Budgeted Sales April (Actual) S7200,000 May 8400,000 June 1 020,000 July 1.080,000 August 600,000 September 900,000 Additional information Cash Sales 40% Credit sales (Collected the following month) 60% Prepare Sales Budget and Cash Collection from customers from May to August Solution:...

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Submit Request Answer ▼ Part C CH3 Spell out the full name of the compound. Submit...

Submit Request Answer ▼ Part C CH3 Spell out the full name of the compound. Submit Request Answer ▼ Part D...

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Periodic Trends V03272017 8. Explain the following: a. lonization energy for nitrogen and oxygen does not...

Periodic Trends V03272017 8. Explain the following: a. lonization energy for nitrogen and oxygen does not follow the normal trend, why? b. Successive ionization energy of an atom increases across the periodic table, why?...

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By syst D+2)x+(D + 2)y to the end of a spring, stretches it 4 inches. Initially,...

by syst D+2)x+(D + 2)y to the end of a spring, stretches it 4 inches. Initially, the mass ih from rest from a point 6 inches below the . Find the of motion g-32 ft/s2 for the xtt)-...

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According to data from a medical association, the rate of change in the number of hospital...

According to data from a medical association, the rate of change in the number of hospital outpatient visits, in millions in a certain country each year from 1980 to the present can be approximated by t'( =0.0014081-1980)0.50 where is the year. a. Using the fact that in 1980 there were 253,477,0...

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In MATLAB Curve fitting Given the following data, find the best linear functional relationship and cubic...

in MATLAB Curve fitting Given the following data, find the best linear functional relationship and cubic functional relationship using “polyfit,” “polyval,” and “plot” built-in functions. Plot all three fits that you got from Matlab. A rough plot by hand is allowa...

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Please help A 2332 3. er wire has a length of 15 m and a radius...

Please help A 2332 3. er wire has a length of 15 m and a radius of 10 x 10 m Calculate the resistance of the wire. The resistivity of copper ρ 1.68 x 10-8 Ω·m. An electric potential of G/V is applied to both end. etermine the current through the wire and pawer created by the curre...

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2. Draw all the resonance forms for the following compounds. Use curvy arrows to show the...

2. Draw all the resonance forms for the following compounds. Use curvy arrows to show the flow of electrons. (8 pts)...

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10-23 Attendance at Physical Inventory Counting. A processor of frozen foods carries an inven- tory of...

10-23 Attendance at Physical Inventory Counting. A processor of frozen foods carries an inven- tory of finished products consisting of 50 different types of items valued at approxi- mately $2,000,000. About $750,000 of this value represents stock produced by the company and billed to customers prior...

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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...

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For the vectors shown below, determine the values of A and the acute angle θ. (in...

For the vectors shown below, determine the values of A and the acute angle θ. (in degrees) that would make-| +Av,--2.5i-4j. Use that θ.-20°, v,-2 and v,-3. Note: The angle θ, is between the vector": and the negative y-axis. y-axis x-axis 2...

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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?...

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(x) (m) Consider the wave shown in the figure. tes 60 40 20 0 -20 -40...

(x) (m) Consider the wave shown in the figure. tes 60 40 20 0 -20 -40 -60 100 300 500 a) Calculate the velocity of this wave. b) Find the wavelength of this wave. ym) c) Find the frequency and period of this wave. d) Write an expression for this wave. tt = 3ss 60 40 20 0 -20 -40 -60 1 100 300 500 -&...

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Propose a reaction that could transform Lindane or part of the molecule (I.e functional group) into...

Propose a reaction that could transform Lindane or part of the molecule (I.e functional group) into a new molecule. Include reagents....