An individual has a side line business as an economics tutor. They model their cash inflows using the continuous stream f(t)=100−10t for t>0. Why is this potentially NOT a good model for a continuous income stream for all t>0?

Q: Consider the following tank-water system. Tank A holds 200 liters of water, initially pure. Brine…

A: The given data has been illustrated in the following figure,

Q: Find the consumers surplus if the demand function for a particular beverage is given by…

A: The consumer surplus is given by C.S.=∫q=0q=eDq dq -e·De, where e is equilibrium value of q. Here,…

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 the local maximum, minimum value and saddle point of f(1, y) = x' + y* - 4xy+1.

A: We will use following  critical point ( maximum ,minimum or saddle point ) of a function occur…

Q: The integrating factor of the LDE y' = x - 2ycotx is

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Q: How might the competitive-hunter model be validated? Include adiscussion of how the various…

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Q: If it costs Microsoft $1,230 to manufacture 8 Kinects per hour for the Xbox 360 and $2,430 to…

A: Given, To manufacture 8 kinects it costs $1,230. To manufacture 16 kinects it costs $2,430. Let,…

Q: Find the linearization of y = at x = 16.

A:

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: 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 positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Consider two interconnected tanks of brine solution. Assume that Tank Y contains 20 litres of water…

A: We are entitled to solve one question at a time and up to 3 sub-parts only. Please post other…

Q: Given the demand function D(p) = 350 – 3p, - Find the Elasticity of Demand at a price of $8 At this…

A: The given demand function is: Dp=350-3p2 To find the elasticity of the demand at the price of $8

Q: find the level of output that maximizes profit,

A: In this question, we find the maximum value of the multivariable function by using second derivative…

Q: Find the orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

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Q: Find the demand function x = f(p) that satisfies the initial conditions. dx 800 x = 20,000 when p =…

A:

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

A:

Q: Suppose that we were to model a continuous income stream using the function f(t)=t2 / (t-1)(t+1) for…

A: The function that models a continuous income stream is

Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

Q: 1. Given the profit function n 160x-3-2xy-2y+ 120y- IN for a fim producing two goods x and y. (a)…

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Q: The regression function r(x) = E(Y|X = x) minimizes E(E((Y − r(X))^2)). Is this true or false?

A:

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: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

A:

Q: the demand function for a particular beverage is given by D(q)=(3000)/((3q+2)^(2)) and if the supply…

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Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: Find the​ consumers' surplus if the demand function for a particular beverage is given by…

A: We are given the demand function for a particular beverage as: D(q) = p=30003q+72 The equilibrium…

Q: The revenue per month earned by the Couture clothing chain at time t is R(t) = N(t)S(t), where N(t)…

A: The total revenue per month at a time t is given by R(t)=N(t)S(t). To find the rate of increase of…

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

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Q: What is the stability of equilibrium points of A and B? Is the energy of B higher than A?

A: If the vector field lines converge to the point or stay close to a point at all times the point of…

Q: Consider the equilibrium O of the continuous-time system given by å = Ax,where A E R²×". Which of…

A: This is a problem of the Dynamical system, a system of the differential equations.

Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: If f is a function of x and y such that fxy and fyx are continuous, what is the relationship between…

A: Function: fx and fy are continuous function. Let us choose f(x,y)=x3y3+πxy Here fx=3x2y3+πy…

Q: Consider a population of tuna T that is growing logistically according to the equation:…

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Q: Construct a suitable Lyapunov function of the form ax? + cy², where a and c are to be determined,…

A: Since you have asked multiple question, according to our guidelines we will solve the first question…

Q: Find the orthogonal trajectories of y² = cx³

A:

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: The weekly demand function for butter in the Toronto- Canada is Qd = 20000 - 500Px + 25M + 250Py,…

A: Given that - The weekly demand function for butter in the Toronto- Canada is Qd = 20000 - 500Px +…

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: V3 (9) 1 x' x(0) = V3 - 1

A:

Q: Although we used gradient descent to find the minimizer of f in part (a), we can also use calculus…

A: Given: fx=12Ax-b22+γ2x22   To show: The minimizer of the given function is, x^=ATA+γI-1ATb

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ f(x,y)= fx(x,y)= Of(x,y)= f₂(x, y) =…

A: We need to find partial derivative.

Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Assume that the demand curve is P = f(Q) = 60 − 0.2Q and the supply curve is P=g(Q) = 30 + 0.3Q.…

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Q: For demand function 2 = a-bP and supply function Q, = dP-c , using Cramer's rule determir..…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Find the critical point(s) of the function f(x, y) = -2r³ – 4ry + 2x – 5y – 1 and classify them as…

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Q: Find the local maximum and minimum values and saddle point(s) of the function f(x, y) = xy - 2x – 2y…

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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 orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: Find the critical point of the function, then determine if it is a local maximum, local minimum, or…

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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.