Set D = {(x, y) ∈ R2: 0 ≤ x ≤ 1, 0 ≤ y ≤√x} and let (X, Y) be evenly distributed on D Calculate P (Y> X). Please explain so I understand to be able to solve similar kind of questions.

Q: (c) Prove the inequality I +y +x > Vryz 3 if x > 0, y >0 and z > 0.

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Q: Given f(x, y, z) = 3x – 2y + 1z, find f. (æ, y, z) = fy(x, y, z) = f:(x, y, z) = |

A: We are given with the function f(x,y,z) and need to find the derivative fx,fy and fz.

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: Using the Convolution Theorem, what is L[h(t)]?

A: In this question, we use the convolution theorem to find the Laplace transform of the given function…

Q: Given f(z, y) = et y" - 2°y, show that fry = fyx-

A: Partial differentiation

Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: Given f(x, y, z) = v- 5x – 3y – 4z, find fa(x, Y, z) = f,(x, y, z) = f:(x, y, z) =

A: Given,          fx,y,z=-5x-3y-4z

Q: 14. Find the distance between the two skew lines. x = 2+t x = 4+s y = 3-t y=1+s z = 4t z = 2- 2s

A: Given query is to find the the distance between two skew lines.

Q: If the joint p.m.f. of X and Y is given byh(x , y) = k(x+ y)2, x = -1, 0, 1 and y = 0, 2, 4.where k…

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Q: Given f(z, y, z) = V31 – 4y + 6z, find fz(x, y, 2) = fy(x, y, z) = f:(1, y, z) = %3D

A: Given :f(x,y,x)=3x-4y+6z

Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

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Q: Given f(x, y, z) = 3x + 6y – z, find fr(x, y, z) = %3D fy(æ, y, z) = %3D f.(x, y, z) = %3D

A: om differentiation we get

Q: If X and Y are independent RVs with f (x) = e U (x) and f,(y) = 3e¯" U ( y), e-3y find f.(z), if Z =…

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Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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Q: If f(x, y) = (xy)", with |xy| < 1, find 2 af af and n=0 fe -y/(1-xy)^2 af -x/(1-xy)^2 dy

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Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

A: Apply formula of trapezoidal error

Q: If D is the distance between the skew lines L:x=1+t, y=1+6t, z=2t L2: x=1+2t, y=5+15t, z=-2+6t, then…

A: here we the formulae   the a plane have normal n→=&lt;a,b,c&gt; and passes through a point (x1 ,y1…

Q: af (x,y) f(x, y)=xe"+* 5 у, Х (а) Сompute y af(x,y) X f(x, y)=xe³"+* ,5 у (b) Compute ду y

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Q: Given f(x, y, z) = 5x² + 3y? + 2z², find fr(x, y, z) = fy(x, y, z) = %3D f-(x, y, z) = %3D

A: We have to find partial derivative

Q: Let X and Y be independent and distributed as N(u, 1). Is T = X-Y sufficient?

A: According to factorization theorem, If the likelihood function L(x,θ) can be expressed in the form…

Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: Given f(x,y,z)=√(−6x+5y+2z), find fx(x,y,z) = fy(x,y,z) = fz(x,y,z)=

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Q: Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

A: We will use definition of differentiation. First we will handle derivative of the root of the…

Q: The distance between the following two skew lines is Line#1: [x, y, z] = [1,1, 10] + t[5, –3,0]…

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Q: Suppose the labor cost in dollars for manufacturing a cabinet is C where x is the number of hours…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: If D is the distance between the skew lines L: x=1+t, y=1+6t, z 2t L2: x=1+2t, y=5+15t, z= -2+6t,…

A: Two lines in space can be skew, parallel and intersecting. Lines are skew if they are neither…

Q: (a) Vx E R, 3y E Z such that y > x + 110. (b) Vx E Z, 3y E N such that y > x + 110. (c) 3x E Z such…

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Q: Apply Euler method and Richardson extrapolation for h = 0.2, 0.1 the problem: and abtain g y' = ty…

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Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

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Q: Given f(r, y, z) = – 5e 4ayz, find %3D fr(x, y, z) = f,(x, y, z) = f:(2, y, z) =

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Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: Given f(x, y, z) = √x2 - z+ 1 = ду 2Va²-z o af Х - z ду ala ala ду = Vx2 ет - У - у2 Y Determine af…

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Q: Given the normally distributed r.v. X with μ=25 and P(X > 10) = 0.9332, then σequals

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Q: 2. Find Df(x, y, z) for f(r, y, z) =x In z+r+ y at (0,0, 2).

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Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: Suponga P(Z,=K) = 2 Determine la distribucioñ de Zn. Ejercicio (DistrbugER del proceso de…

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Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: An unevenly heated metal plate has temperature T(x,y) in degrees Celsius at a point (x,y). If…

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Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: If X is a RV with f(x) = 0, when x 0, P(X 2 a) <u/a. %3D

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Q: The diagonals of square LMNP intersect at K . Given that LK=1, find KN . 1 K KN =

A: For the following given question  Given,  LMNP is a square  and LK=1 then,

Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

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Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.