Suppose that we were to model a continuous income stream using the function f(t)=t2 / (t-1)(t+1) for t>0. Why is this potentially NOT a good model for a continuous income stream for all t>0?

Q: A soccer ball manufacturer is planning to expand its workforce. It estimates that the number of…

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Q: 20. In "x" years from now, one investment plan will be generating profit at the rate of R₁ (x) = 50+…

A: Given: R1x=50+x2R2x=200+5x

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: Given function f(x)=mx+b where m and b is constant our aim To evaluate linearization of f(x) at…

Q: Find a point c satisfying the MVT for the given function and interval. 2 y = x3 [0,8]

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Q: Suppose a company wants to introduce a new machine that will produce a marginal annual savings in…

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Q: Suppose a man is 30 years old and would like to retire at age 60. Furthermore, he would like to have…

A: In the question  it is asked to calculate the amount of money that a person would save in order to…

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx +b at any given…

A: Givenf(x)=mx +b where m and b are constantsTo find linearization of f.

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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Q: Find the present value of a continuous stream of income over 3 years if the rate of income is…

A: Given the rate of income , ft=80e-0.08t Number of yearsT=3 Interest rater=11% The present value can…

Q: A person has a direct utility function as follows: u(x, x,) a) Find the expenditure function and…

A: Given, direct utility function: ux1, x2=x1x21+x2 We need to find the expenditure function and…

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

Q: Suppose that t years from now, one investment plan will be generating profit at the rate of…

A:

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: given S'x=150-x2C'x=x2+114x where S'x is the rate of annual saving and C'x is the rate of annual…

Q: 5. Show that the two functions yn = Aet (interest compounding) and y2 = Ae (discounting) are mirror…

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Q: Use the basic equation for the capital asset pricing model (CAPM) to Find the risk-free rate for a…

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Q: Find the marginal revenue function. R(x) = x(18 - 0.04x) R'(x) =D

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Q: It is estimated that between the hours of noon and 7:00pm, the speed of highway traffic past a…

A: Check S(t) for all values of t

Q: The current toll for the use of a certain toll road is $2.50. A study conducted by the state highway…

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Q: The function F(x) = 2x^3 + 3x^2 has a relative minimum point at x =

A: We will solve the problem

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

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Q: Suppose that a population has a rate of growth of 0.1 and a carrying ranacity of 2 million, Şet up…

A: The population dynamics can be modeled through a first-order differential equation. It contains the…

Q: a. What are the net total savings during the first year of use of the​ machine? b. What are the net…

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Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: Given that

Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: Show that the function f(x) = e^-x^2/2 has a relative maximum at x = 0.

A: Given function is: fx=e-x22 Differentiating f(x) with respect to x we get, f'x=e-x22×-2x2f'x=-xe-x22…

Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

A: Given problem:- The population of the world in 2015 was 9.75 billion people and was growing at a…

Q: A bacterial population B is known to have a rate of growth proportional to B itself. If between noon…

A: We will use the exponential growth equation of bacteria .

Q: 4. A company possesses a major piece of equipment that denigrates at a continuous rate f = f(t),…

A: (a) Let F(t) be an antiderivative of f(s) Mathematically, it means: F'(s) = f(s) By Fundamental…

Q: Find the PV of an income stream paying out continuously at a rate of     5000e−0.1t dollars per year…

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Q: Consider the production function:           Y = 0.75X + 0.0042X2 – 0.000023X3 (a) At what level of…

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Q: Find the minimum value(s) of the function f(x) = e* – 2x

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: find a linearization at a suitably chosen integer near a at which the given function and its…

A: (1)Given:

Q: Suppose that a business provides a continuous income stream with an annual rate of flow at time t…

A:

Q: Find the present value of a continuous stream of income over 4 years when the rate of income is…

A: Given, Rate of income per year is $35000. Interest rate is 4%. Here we shall use the formula for…

Q: suppose that a five year rate of projection growth of population trends suggests that t years from…

A: Population of certain community as a function of years “t” is given as follows:P(t) = -t3 + 9t2 +…

Q: Suppose stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two…

A: Given: stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two…

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: The given function is: f(x)=mx+bSo,f'(x)=m

Q: If f(x) = x - ka 1 has a relative maximum at r = -2, then the value of k is

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Q: Given two inputs X1 and X2 with prices W1 and W2 respectively and a production function Y=f(X1,X2),…

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Q: For what value of k will x + k/x have a relative maximum at x = -2?

A: Given: f(x)=x+kx

Q: 2. A property agent handles an office building with 50 identical offices for rental. Experience…

A: 50 offices occupied corresponding to $800 49 offices corresponding to $820 Plot the two points and…

Q: uppose that a machine's production can be considered as a continuous income stream with annual rate…

A: Given,A continuous income stream with annual rate of flow at time t is given byf(t( = 10,000 - 800t…

Q: 2) Show that X₁ = Xo {1+¹*exp(-)} -DC₁ = v(C₁-Cs). satisfies the steady state growth concentration…

A: Given  -DCL'=vCL-CS

Q: Show that the two functions n = Ae" (interest compounding) and y2 = Ae (discounting) are mirror…

A: Mirror image w.r.t y axis: If f(x) is a function then its reflection about y-axis is given as f(-x).…

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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Q: 12. Find the profit function for the given marginal profit and initial condition. dP = -40x + 290,…

A: Solve the following

Q: Find the PV of an income stream that pays out continuously at a rate R(t) = $5000e0.1t /year for 7…

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Q: If (a,B) is a saddle point of the function f(x,y)=21y2-y3+3x2-6xy, then a+ß=

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Q: If a company's marginal revenue function is  MR(x) = xe−x/9,  find the revenue function. [Hint:…

A: Consider the given marginal function.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.