Show that Var (XY) = XY2-(XY) provided. X and Y statistically independent.

Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

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

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Q: 5. Evaluate the integral 2 c2x x2 (x² + 2y³) dy dx.

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

Q: 7 Find the most general antiderivative for the function – 5VP. 2 -

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Q: find integral x3 3) S dx /1-x²

A: We have to find the indefinite integral

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: Evaluate L 8y (x³ + 1)² 2y by reversing the order of integration. dady

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Q: Evaluate J S S dydx. r4x Jx2

A: To solve this question first integrating with respect to y and plug in the limit then integrate with…

Q: i) Find the critical numbers of function f (x) = x/x+3 TV. ii) If 2x- y=k is the equation of a…

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Q: Show that | S f(2) dx| < Sa \f (x)| dx.

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Q: (2 dr z²–10z+15) Integrate:

A: NOTE: Refresh your page if you can't see any equations. . take long division

Q: Find the most general antiderivative. 9 dx -x2 x zX - IN

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Q: (b). Evaluate the integral 6x Vx +4 dx.

A: Part(b) Given

Q: Evaluate the integral S√x Inx dx 3 2 4 -x² Inx+ x² + C 03x³nx-x²+c 4 2 -x² Inx+ 2 C 15 3 2 4 °²x²nx…

A: We have to solve above integral

Q: Minimize S = xy + xz + yz subject to xyz = 3 v

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Q: Find the simplest integrating factor u(x) of - xy' = (8x + 9)y + x In(x). µ(x) = %3D

A: As the given equation is an first order differential equation ,we can find integrating factor.

Q: Find the total differentials of w=2z2 ysinx

A: The detailed solution is given below Thank you

Q: 2 Evaluate the integral S (3x³ – 2x² + x) dx. 1

A: We solve it by integrating polynomial

Q: 1 V5x + 4

A: We have  ∫1x dx=2x.

Q: Find for following 1.y = (x + v3x)S

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

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

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Q: Evaluate the integral. S. sec Sx dx sec 8x tan 8x - In|sec Sx + tan Sx| + C 1 sec 8x tan 8x + In|sec…

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Q: of of and ду Find f(x,y) = Vx + 3y?

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Q: Find two positive numbers x and y that minimize the product xy, and satisfyx + 4y = 120.

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Q: 2 V4 – x²dx 0.

A: A detailed solution is given below

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

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Q: Find all local extrema for 4 f(x, y): * - 4xy + y.

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Q: Find an antiderivative of (3x3+9x5)/x6 in the variable x where x does not equal 0.

A: From the given problem:   3x3+9x5x6   So,    3x3+9x5x6=∫3x3+9x5x6dx   We can simply write as:…

Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: Find the marginal PDFS fx (x) and fy(y).

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: x²-2x* 5. Integrate with respect to x x4

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Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

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Q: Find the most general antiderivative of f(x) 2x-1+x.

A: Given,            f(x) = 2x2 - 1 + x-2

Q: 5. Evaluate by using beta function: | °(1 – r*)} dx.

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Q: Find an antiderivative F(x) of f(x) = 7x – Vx.

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Q: 5. Use integration by parts to evaluate dx. (x+1)2 Hint: Choose u = x.

A: Given that ∫xx+12dx∫xx+1-2dxNote : integration by parts∫fxgxdx=fx∫gxdx-∫dfxdx∫gxdxdxfx=x…

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: 1. Evaluate S x³V1+ x² dx using Integration by parts.

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Q: evaluate using Integration by Parts.

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Q: Consider a risk process with X, ~~ y(2, 2) with loading factor 15%. Using the approximation eR* * 1+…

A: Solution

Q: Consider the function f(x)=5x^9+5x^6−6x^3−8Enter the antiderivative of f(x)

A: Given function is

Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

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Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.

Q: the integral (dx)/(xsqrt4x2+1)

A: