NUMBER 4solution should be written clean and clear. thanks 3. Dwight is selling baskets of beets. If the profit in selling x baskets is400P(x)200x²3200x ++1000and the price-demand function is given by p(x)the 21st basket of beets.4. Use L'Hopital's rule to evaluate50+sinh(2)limx0 sec(x) - 1200x3Estimate the cost of producing

we have to evaluate limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Answered: 4. Use L'Hopital's rule to evaluate…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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If y is a function of x and the slope of the function is zero at x=10 then to determine that y reaches a minimum dy/dx must be ............... at x=10
Suppose the marginal propensity to consume is given by: DC/DY=.03- .2/Square root of (y), (in billions of dollars) and national consumption is $8 billion when disposable income is $0. Find the national consumption function.
Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.002x^3+0.07x^2+15x+600, and currently 90 chairs are produced monthly. a) What is the current monthly cost? b) What is the marginal cost when x=90? c) Use the result from part (b) to estimate the monthly cost of increasing production to 92chairs per month. d) What would be the actual additional monthly cost of increasing production to 92chairs monthly?
The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given byƒ(t) = 500e0.1t,under certain storage conditions, where t is time in days after packing of the product and the value of ƒ(t) is in millions. (a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take?(b) If t = 0 corresponds to January 1, what date should be placed on the product?
Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a, then the linearization of ƒ at x = a is also the quadratic approximation of ƒ at x = a. This explains why tangent lines fit so well at inflection points.
Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.007x^3+0.07x^2+15x+600, and currently 70 chairs are produced monthly. a) What is the current monthly cost? b) What is the marginal cost when x=70? c) Use the result from part (b) to estimate the monthly cost of increasing production to 72 chairs per month. d) What would be the actual additional monthly cost of increasing production to 72 chairs monthly?
Suppose that the marginal propensity to consume is dC dy = 0.02 + ln(y + 1) y + 1 (in trillions of dollars) and that consumption is $6.04 trillion when disposable income is $0. Find the national consumption function.
In a certain company, the income from the sale of x thousand pieces of products is given by I (x) = 9x, while the cost of making the same x products is given by C (x) = x ^ 3-6x ^ 2 + 15x + 1. Assuming that I and C are in thousands of dollars and everything produced is sold, what is the maximum profit the producer can make? Argues using first or second derivative criteria.
Suppose that the marginal propensity to save is dS dy = 0.95 − ln(y + 1) y + 1 (in billions of dollars) and that consumption is $6.03 billion when disposable income is $0. Find the national consumption function.

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4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1