Problem 1. The Cook's distance is defined as Please show that Di = (Y - Y,))(Y −Y)) (p+1) MSE Di - (+²) (A) = 1 - hi where ri are internally studentized residuals.

Q: 5. Show how the origin changes stability as a changes by using the Poincaré Diagram. x - [i :]• 2 a…

A: The stability of fixed points of a system of constant coefficient linear differential equation of…

Q: Differentiate. F(x) = (6x + 1)? %3D F'(x)= %3D

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Q: d²x 4. + xe0.01x = 0. JP x(0) = 1, x'(0) = 1; x(0) = 3, x'(0) -1

A: Given that d2xdt2+xe0.01x=0, x0=1,x'0=1; x0=3,x'(0)=-1. (i) So, the equation can be written as,…

Q: 2) Find the clamped cubic spline for the data (1.1).(3,4), using that f'(1) - 2.f(3) = 5

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Q: 2x2 Use the Quotient Rule to find g'(1) given that g(x) = 6x +11 %3D g'(1)=D (Simplify your answer.)

A: Given Data: Function: gx=2x26x+1 The quotient rule of the derivative is, ddxfxgx=gxf'x-fxg'xgx2

Q: 13. Calculate, where Som fx (w > fy (8-w) dw -16 окус). fx (x) = { 1 + 0xxx/ fyl2)= { 0, othmasid. !…

A: Given: fxx=1,0<x<10,otherwise   . . . (1)…

Q: 5. Which is the inverse of f(x) =2? %3D Or (2) = H 241 Of (x) = 1- Of (x) = 1 1-c f(x) = 1+a

A: To find f-1(x) We interchange x and y and solve for y as function of x

Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 9(a). Suppose that in the "water and plant growth height" example we have four plants in the…

A: The following information has been given: 9(a.) x y 1 6.4 2 6.6 3 7.6 4 9.4 9(b.)…

Q: Problem 13. Let f(x) = 2sirtx) %3D f'(x) =

A: We know that; The Chain rule: fgx'=f'gx·g'x And ddxax=axlnaddxsinx=cosx   Given: fx=2sinx

Q: 7. If g(4) = 3k +7, g(9) = 7, g' is continuous and %3D J g'(x)dx = 2k? + 13, find the value of k.

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Q: * The following statement will be used for Problems 2-5 * A UCF mathematics Professor sampled a…

A: Important points for the question: 1.  f'(x) = slope 2.  p ∈ (0,1) means 0<p<1 means p is less…

Q: (1-))csc²( 1– y)dy

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute…

Q: 21. Let h(x) = tan(5x + 6). Then %3D h'(2) is and h"(2) is

A: 21) The given function is: h(x)=tan(5x+6) To find h'(2) and h''(2)

Q: 4. Find the equation of the tangent line and the normal line to the graph of the given function at…

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Q: 2. Evaluate aydA, where R = {(x, y) : 4 ≤ a² + y² ≤ 9, a ≤ 0, y ≥ 0}. x R

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Q: 12) Find the clamped cubic spline for the data (1,1),(3,4), using that f'(1) = 2, f'(3) = 5

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Q: 5. Exact Differe ntial Equation: x(3xy-4y' +6dx+(x' -6x'y' -1dy = 0

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Q: 5. For y=x2 -x, the graph is given (a) mark two points on the graph, one with x1=3 and one with…

A: The equation of the function is y=x2-x. Given a point with x1=3 and another point x2=3+∆x. The…

Q: 1 and y' CO)

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Q: Show that the vector in B4 is orthogonal to the vectors in B1, and that the vector in B2 is…

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Q: Find the equation of the normal line to the graph of e tan(ry) – In(r – 3y) = sin (7z) at the point…

A: Solution is written in below steps.

Q: 10. x 유 3 4 X, x, x(0) = (2 ; see Problem 2.

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Q: Klein is located on the tangent line to y=3x2 -x  at x = 1.

A: Using , slope point formula

Q: Q.69 Equation of the line normal to function f(x) = (x-8)2/3 + 1 at P(0, 5) is

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Q: a. Given In() in(†) A. Find the equa B. Find the equa

A: (A) Given equation is: lnxy+y3-2x=-1 Differentiating both sides with respect to x we get,…

Q: Problem 1. Let X ~ Gamma(a = 2, 0 = 2). Compute: (1) VaRo.975(X) (2) ex(9.488) (2) TL 1 TVeD (Y)

A: From the given information, X~Gamma(α=2, θ=2) fx=122Γ2x2-1e-x2, x>0      =14xe-x2, x>0 1.…

Q: 1. If ß be the angle between the lines of regression, show that tan B = (1 -) 0,0/r (o, + o,).…

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