Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices (- O), (0,1). (This means their joint PDF is a constant). Find the joint PDF of X and Y, call if f (x,y). Find fy (y)

Q: Find the Partial Derivatives of the functions with respect to each variable X+y 6) f(x,y) = -у' -1…

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

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Q: Find the derivative of y with respect to x. (Hint: chain rule) y = -csc-1 24 V(8x + 92 - 9 24 (8x +…

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Q: find the partial derivative of the function withrespect to each variable.35. ƒ(t, a) = cos (2pit -…

A: The given question is taken from the partial derivative in which we have to find the partial…

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

A: Given: y=xy ⇒y=x12y12 ⇒y12=x12

Q: Find the local maximum, minimum and saddle points of the function using the second derivative test:…

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Q: If X and Y have joint pdf given by

A: From the given information, fX,Yx,y=2I0,yxI0,1y                =2, 0<x<y, 0<y<1

Q: Find the indicated partial derivative(s). f(x, y) = x7y8 – x6y7; fxxx, fxyx fyxxx(x, y) fxyx(x, y)

A: We have to find the partial derivative

Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: Find the Partial Derivatives of the functions with respect to each variable 3) f(xу) - (ху-1);* Ans.…

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Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

Q: Find the partial derivative. f(p, q) = ev af

A: From the given problem; fp,q=e6pq As we know that: The chain rule: fgx'=f'gx·g'x The Power rule:…

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: Find the first partial derivatives of the function. u+ aw du

A: In The partial derivative of w with respect to u, functions of v are treated as constants. In the…

Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: Use variation of parameters to find a particular solution of the ODE y" – y = 2e".

A: Given differential equation is  y''-y=2ex we have to find  the particular solution of this…

Q: Find the first partial derivatives of the following function. s(xz)-z2 tanxz

A: The given function is s(x, z) = z2 tanxz.The first partial derivative of the function s with respect…

Q: of ) Find the first order partial derivative of and for the function f (x, y) = x/y -x²y+y² ây

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Q: Find the partial derivative. z = (2² + 2x – 6y)"

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Q: How many second partial derivatives does f(a,b,c, d) have?

A: Let p=fa,b,c,d. Note that, for a function of two variables p=fa,b there are four second partial…

Q: Find both first partial derivatives. z = cos(10xy) az ax az ||

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Q: compute the derivative. y = z csc(9z + 1)

A: y=z csc9z+1

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: Find the Partial Derivatives of the functions with respect to each variable 8) f(x, y) = In(x +y)

A: When take partial derivative with respect to one variable consider other variable as constant.

Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

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Q: 4. Find the first partial derivatives of the function. z= xsin(ry)

A: We will use the formula  (uv)'=uv'+u'v Given z=x sin(xy) Then the partial derivative with respect to…

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

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Q: 1. Find the directional derivative of the scalar function f = yzx^2 + 4xz^2 at the point P(1,-2,-1)…

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Q: Find the first partial derivatives of the given functions

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Q: Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices…

A: From the given information, Vertices of a triangle are as follows: A =(-1,0) B= (1,0) C= (0,1)

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: Find both first partial derivatives. Z = In

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Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: Use the Chain Rule to compute the partial derivative. би +о In (3u? + uv) = 3u + uv

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Q: Find the partial derivatives of the function with respect to each variable.

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Q: Find the first partial derivatives of the funct f(x, y) = x8 + 7xy5 fx(x, y) =

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Q: Find all second-order partial derivatives for ƒ(x, y) = -4x3 - 3x2y3 + 2y2.

A: To find all second-order partial derivatives for f(x,y)=-4x3-3x2y3+2y2.

Q: 04:- Use the Chain rule to find the derivative ) of z = 3x2 - 2 xy y and If x=x (u, v) = 3u + 2v and…

A: Please refer to the image below.

Q: find all the second partial derivatives of Z and show complete solutions Z= tan-1 ( x2 / y3 )

A: Partial derivative of the function Z=f(x,y) is denoted as The first partial derivative∂Z∂x, ∂Z∂y The…

Q: Find all the first and second order partial derivatives of f (x,y) = 10 sin (2x+y) + 3 cos (x−y)…

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Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given

Q: If a pdf of Y is ƒ(y)={1-|>| ||S1' />1 find and graph F(y).

A: Given, f(y)=0  y>1 From the above expression, Thus, the function is zero (f(y)=0) in the…

Q: az (8) Find variables z and y and partial derivative exists. if the equation yz – In z = x² +y?…

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Q: Find the partial derivative of fy for the function * 3 f (x, y) = (3x² + y²) ³ 3x² (3x² + y²)²…

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Q: Find both first partial derivatives. z = x2e2y

A: Given function is z=x2e2y. Partial derivative means derivative of function with respect to one…

Q: Find all possible functions with the given derivative. 1. If y 1, then y %3D 2. If y = a, then y 3.…

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Q: End fz(3) in terms of the joine pdf of X and Y if

A: From the given information, Let, f(x) be the density function of X. f(y) be the density function of…

Q: It follows that the pdf of Y is

A: It is given that the  X has a geometric distribution with parameter p i.e. X~G(p) and fX(x) =qxp ;…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.