59. Show that if f(x) = rx +s is a linear function (r, s constants), then TN = endpoints a, b. f(x) dx for all N and all

Q: ive of f(x, y, z) 1) in the dired

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Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

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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…

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A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

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Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: Suppose we have a revenue function given by R(z) = 6z- az?, %3D = 10? where a is a constant. What…

A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

Q: Find a point c satisfying thr MVT for the given function and interval  y=x/x+2 [1,4]

A: Given query is to find the value of c.

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: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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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: Determine two functions, defined on the interval (−∞,∞)(−∞,∞), whose Wronskian is given by…

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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: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: If the utility depends only on the consumption of x and u (x) = ( 2a¯i + 3) (-4xi +2), is Marginal…

A: Given u(x) = 2x-12 + 3-4x14 + 2

Q: xy ,show that: x- y If z = = 0

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Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

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

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Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: Let y=2x^2+3x+3. If Δx=0.1 at x=4, use linear approximation to estimate Δy Δy≈

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Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: Find f, and f,. f(x, y) = 13x In xy

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Q: How can we minimize the error of an approximation in a linear approximation at the point (a. ƒ (a))?…

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Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm:…

Q: Find the limit of function f (x, y)D. at the point (0,0) through the path x=y². а. О b. 1 8 d. does…

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Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

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Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

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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: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: Suppose f and g are two differentiable functions such that f(9(x)) = x? and supposed the equation of…

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Q: 2. Use a linear approximation to estimate V1.03. 3 If f and a are the functions whose gronhs

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Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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

A: Given: y=mx+b

Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: Consider the function y defined implicitly by 3(x2 + y2)? = 100xy. Use the linear approximation at…

A: Given : 3(x² + y²) = 100xy

Q: . Suppose that we don't have a formula for g(x), but we know that g(2) = 4 and g'(x) = Vx² + 5 for…

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Q: Find a function f(x) whose linearization would help me come up with an approximation to 4 26

A: We want to find the function,  It's form is ,L(x) = f(a) + f'(a) (x-a)  We approximate 4/26 ~ 4/25…

Q: 4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) =…

A: Given x2+3xy2+y3=9y2=-1

Q: If ø = 3r²y – y³,2. Find gradient Vø at the point (1, –2, –1).

A: The solution is given as

Q: 4. Let F : R² → R² defined by F(x,y) = (2x +3y, –x +y). Is F a linear? Why?

A: Given

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

A:

Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.