(a) Assume that traffic flows at a rate of 240 vehicles per hour on the stretch of road between intersections D and A. Find and X3- the flow rates X, X2

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

A:

Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: Consider the given function. fx,y=2xy+y2+2x-1 Find the derivative with respect to x. fx=2y+2 Put the…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Find y' for y = vTy at the point (9,1).

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Find the value of the number such that the families of curves  y =(x+c) -1  and y = a ( x+k) 1/3 are…

A: Given,

Q: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: Show that B is a linear function of Y,, Y2. Yn Show that B is conditionally unbiased.

A: The regression model is  Yi = βXi + ui We have to show that β is conditionally unbiased.

Q: y = x – 2 + Ce* X-

A:

Q: Find the linear approximation of f(x) = e(a) at a = 1.

A:

Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: Find the best linear approximation to f(x) = x² on the interval [0, 2].

A: Here we use Taylor's approximation.

Q: Find the slope of the curve y=x2−3x−4 at the point ​P(2​,−6​) by finding the limiting value of the…

A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 50 + 7x2 + 8y2, where x…

A: Differentiate wrt x and y

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

A:

Q: What is the linear approximation of the function f (x) = e x at x = 1?

A:

Q: Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2?2 + 6? +…

A: Given, Total cost of manufacturing x units of a certain commodity =  C(x) =  2x2 + 6x + 12 We need…

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Find the linear approximation to f(x) = at a = 4.

A:

Q: Find the linearization L(x)of the function at a .

A:

Q: Let f (x,y,z) = xln(yz). Find the maximum rate of change of f at the point (1,2,;) and the direction…

A: Suppose f  is multivariable function as f=fx,y,z then gradient vector is a vector that is composed…

Q: 3- If the value of elasticity is equal to Ey = 0.21 then the ., note that 11.5 = xi = 10, yi %3D…

A:

Q: Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

A:

Q: The student should determine the minimum rate of change of the function g(x, y) = y²e*Y on the…

A: First I have written the rule of minimum rate of change of a function at given point and then find…

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a 6

A:

Q: (8) Find the linear approximation of the function f(x) = Va at a = 25 and use it to approximate the…

A:

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

A:

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 6x2 + 6y2, where x…

A:

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation to approximate the…

A: Given: hx=x4 To approximate the values of 34 and 44 using linear approximation of hx. Note: the…

Q: The gravitational attraction F between two objects of masses m1 and m2 is jointly proportional to…

A: see the attachment for answer

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: (c). If y = f(x1, x2, u, v), where x =h(u, v) фу and- pu Find total derivative Also draw their…

A:

Q: obtain a slope field and add to it graphs of the solution curves passing through the given points.…

A:

Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

A:

Q: Obtain a slope field and add to it graphs of the solution curves passing through the given points.…

A: The point is given as x0 , y0 The slope is given by value of dydx at y = y0 Also the equation of…

Q: (c) Suppose that two of the pipes become blocked so that x3 = 0 and x1 = 0. Determine the flow rates…

A: Topic - flow diagram

Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

A:

Q: Find the minimum and maximum values of y = V120 - V6 sec e on the interval [0, ] fmin fmax

A: Solve

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. V35.63 2

A:

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: obtain a slope field and add to it graphs of the solution curves passing through the given points.…

A:

Q: . Find the linearization of √ x at a = 49. Then use your linearization to approximate √ 56.

A: I am going to solve the given problem by using some simple calculus  get the required result.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.