Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

Q: Exercise.1 Find the roots for V8 and V-1

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: 1. find the linear approximation to /(x) at x = Xg. Use the linear approximation to estimate the…

A: Linear approximation

Q: Consider the function f(T,y) kr - 2ry +y2. %3D 1. Show that (0, 0) is a critical point of f(T, y).…

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Q: 3. Let f(r, y)- e (a) Verify that (0, 0) is a critical point. (b) Is this critical point a local…

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Q: Show that (0,0) is a critical point of f(x,y) = x2 + kxy + y no matter what value the constant k…

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Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

Q: Consider the function f(T,y)= kr - 2xy + y?. %3D 1. Show that (0, 0) is a critical point of f(T, y).…

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Q: 8. Let f(x,y) = x² – 8x + 2y? + 4y +7. - a. Find and classify all critical points of f. b. Does f…

A: I have used first derivative rule to find critical point and for classification I used second order…

Q: f (x, y) = 5ye" – e5x – yð

A: for critical points equate the first derivative wrt x and y to zero.

Q: Find constants a and b so that the minimum for the parabola f(x) = x- + ax + bis at the point (5,…

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Q: 1.Test the function def ined by f(x.y)=xlnx- ylnx for its homogeneity. If it is homogeneous, give…

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Q: Let f(x, y) = cos(x)cos(y). Find all critical points of f which lie in the square {(x, y) ∈ R2 : −1…

A: f(x,y) = = cos(x)cos(y)At critical points, partial derivatives of f (x,y) w.r.t x and y are…

Q: A) Show that from the lower relations near the point (0,0,0, 0) u can be written as a derivative…

A: Given relations: vcos(y)+xcos(u)=0 ucos(x)+ycos(v)=0 To find the second order Taylor polynomial of u…

Q: Use Newton's method (2.12.4) to find the minimum value of the lunction f(x) = x + x,x, + (1 + x,)'…

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Q: f(x) has local minima at x = i and x = i f(x) has a global maximum at x = i f(x) has a global…

A: The critical points of any function are the points where the derivative of any function vanishes or…

Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δt =0.006t2. At time…

A: According to the given information, it is required to determine the value of m.

Q: Find the maximum value of  f(x,y)=3xy(5−10x−5y) over the triangle with vertices (0,0), (1/2,0) and…

A: Given :            f(x, y)= 3xy(5-10x-5y)            Vertices (0, 0) (1/2, 0) and (0, 1)

Q: Find the absolute maximum and minimum values for f (x, y) = 5 sin(x) + 9cos(y) on the rectangle R…

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Q: Test the function def ined by f (x,y) = - x- 4y for its homogeneity. If it is homogeneous, give its…

A: Find your answer below

Q: (a) Find the critical point of f(x, y) = (4x2 y) (x² + 4y). (x,y)%3D (b) Find the discriminant, D(x,…

A: f(x, y) = 4x2-yx2+4y

Q: Define the function f: R? → R by f (x, y) = 2xy² – y² – 2x². a) Find the critical points of f. b)…

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Q: f(x, y) attains a global maximum at a point in the interior of R (that is, at a point in R that is…

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Q: A tank hold 300 gallons of brine solution. Brine is pumped into the tank at the rate of 3 gal/min…

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Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

Q: Consider the function f(z,y) = kr?- 2ry +y?. %3D 1. Show that (0, 0) is a critical point of f(z, y).…

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Q: Find the maximum and minimum values attained by f(x, y, z) = 2xyz on the unit ball x2 + y2 + z2 < 1.…

A: fx,y,z=2xyz on the unit ball x2+y2+z2≤1 gx,y,z=x2+y2+z2-1 ∇f=∂f∂x,∂f∂y,∂f∂z ∇g=2yz,2xz,2yx…

Q: (b) Show that the roots of y'(x) = 0 are x = 0, x = L, and x = L/2, so it follows (why?) that the…

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Q: 1 Verify Eular's theorem for z=- =(x²+xy+y*)' x²+xy+y² 2

A: The expression z=1x2+xy+y2=x2+xy+y2-1. We have to verify the Euler's Theorem.

Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: Assume that after  months, butterflies’ populace  in 1000 is calculated as:…

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Q: 3. To understand the spacing between fish in a school or birds in a flock, scientists have defined…

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Q: The function f(x, y) = L(x, y) = arctan(x + 2y) can be approximated by the linear function = ax + by…

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Q: Find the maximum value of f(x, y, z) = y - z Subject to x + y + z = 1,x² + y² = 1 O - √5 + 1 O-√5-1…

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Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: 7. Let f(x, y) = In(x)+2 ln(y) – x – 4y. Find the critical point of f and determine if it is a local…

A: Let's find.

Q: + A(- for 0<x< 1, then u attains its maximum in the interval 0 sxs1 either at x=0 or at x= 1.

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Q: Find absolute maxima and minima of the function f(x, y) = x² + y² on the closed triangular plate…

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Q: 3,4 Find the maximum of the Xy z°t* when all the variables X, y, Z and t are all positive and…

A: We have to find out the maximum value ofxy2z3t4

Q: Given the function y"=-6X(x²-ax+4) (x+a)³ (x -1)³ 3. with (X+2)(x-) - analysiS Enclude all maximums…

A: given that y=-x3x+2x-2find the maxima and minima for the given function

Q: let fie) - 71* Ihen f has a stotionary point at z- The stationary point is CNo arswer given Oa local…

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Q: Consider the function f(x,y) = 3xe" – x³ – e3y. (a) Show that f(x,y) has exactly one critical point…

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Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δ# = 0.006t*. At…

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Q: Consider the functions f(x, y) = x2 − y2 and g(x, y) = x2 + y2 .                             (a)…

A: Given functions are f(x,y)=x2-y2  and g(x,y)=x2+y2.

Q: Suppose ƒ is differentiable on (- ∞, ∞) andƒ(5.01) - ƒ(5) = 0.25. Use linear approximation to…

A: Given:        Suppose ƒ is differentiable on (−∞,∞) andf(5.01)−f(5)=0.25

Q: a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b) Consider…

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Q: Suppose thát the share of total production consumed by player i is x / x+(n1)y, where is player i's…

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Q: ind the orthogonal trajectories of x^3=3(y-c)

A: Given equation of curve  is   x3 = 3(y-c)  we have to find  the orthogonal  trajectories

Q: Let f(x) = e2sinx 1. Use the local linear approximation of fat x = 0 to approximate e2sin (0.01)

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Q: 1. independent in the interval I=(-5, 10)? Are the functions y₁ (r) = max(0, z), 32=1 min{0, z), and…

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