3 Rnd the lineasion of the hunctran f(xLcos line asiz l

Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: az az and at the point (-1, -3, -2). Suppose ry z - 94 = 4xy – z. Compute ду dz |(-1,–3,–2) az…

A: An important result from advanced calculus, called the Implicit Function Theorem,states the…

Q: Use Newlon's Me thod with the runclion $r(x)=x^{2}-2$ and inilial value $x_{0}=3: to calculate…

A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

Q: b) Evaluate the intergral. Show (with your work) that it is Cunvergent and give its Value or that it…

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Q: Prove that (RUS) (TUW), if we know as given from the problem that: RCT and SEW Justify each line of…

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Q: 2) Show that the cosine(45°) = V2 * (0.707). Let “u" = 22.5°, use calculator. %3D - 2

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Q: 5.Use thelefinition to Rrave that Jw wh- 2

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Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: Find the meteix A of the Lineak teansfoRmati on foom IRto IR . 2. given by x2

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Q: xy If z show that: x- y

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Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

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Q: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).

A: The given line segment from   to   can be represented parametrically as: , , and , for    Using the…

Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: 3e dt 10. SET A.

A: We will use the concepts of definite integral

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: Find the ared of the reyion R bound ed.by and the liney=x+2 2. 2. =y-yand the line y--x ......

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Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

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Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

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Q: Compute Jx²z ds where C is the line segment from (0,6,–1) to (4,1,5).

A: The objective is to compute ∫Cx2zds where C is line segment from  0,6,-1 to 4,1,5

Q: 4: verify that wy = Wyx . ریاضيات المرحلة الثانية a w = In (2r + 3y) %3D

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Q: 6) MLATU = 45°, mZSTU = 120x – 1, and mZSTA = 73x + 1. Find x. %3D %3D T. U A

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Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Find the angle (in DMS) between the line L1 through the points P1(2, 1, 4) and P2(–1, 4, 1) and the…

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Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

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Q: ==, j= 4 and x=0 about tue liney=5

A: Disk method: -  When the axis of revolution is the plane region's boundary and the cross-sectional…

Q: 4 Compute the orthogonal projection of u= 3 onto the line L through and the origin. projz (5) =

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Q: 2+ A, BE Muce) such That Ais normal and Hermi tian .Prove That 1ABII - 1BA|/ B is

A: Normal matrix: A matrix A∈Mn(ℂ) is said to normal if AA*=A*A. Hermitian matrix: A matrix B is said…

Q: Express E: livenr coumbination of Ÿ; = and V as a

A:

Q: let z- 5 dy By chain Ruie

A: Given z = √x dy/dx = (1/2√x)•(dy/dz) We have to find d2y/dx2 .

Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: 4. (entroid š pon! of intersetion of 3 mudiens of A hriangl. FAE Ba =/3 DE AG =43 AD (ent roid ond…

A: A triangle ABC, with median AD, BE &amp; CF concurrent at centroid G. Also, AG = 23ADBG = 23BECG =…

Q: Compute 1. % 1+ vår + g2 dr, lal 2 1+ " 2. 1+ V2r-

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Q: 12) Show that D- ldi-dal between is shortest distance a x+ by + e2 of i ancd ax +by +Cz = dz?

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Q: Find the maaimum and miniryem Valiaes of e feencteon Cif exits) feny) Luž-3ary

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Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Selve the fallowing euler Cauchy.eg:using net hed of variation? O xy.3x y+ 6X.y-6y= Xs,in X 2. %3D

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

Q: Compute Cixj)xk and un h Find patro of he pMane gog ingi (-i, novmetit tj 4K

A: The equation of the plane passing through the given point and perpendicular(normal) to the given…

Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

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Q: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

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Q: Compute the orthogonal projcction of V 10 onto the line L through -3 and the ariqin. 6 ,4

A: Projection

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: If a = i + j + 5k and b = i + j + 3k, compute the cross product aXb

A: We have to find cross product

Q: Construct a linear map L(z) = az + 6 that will send the imaginary y-axis to the line v = - u

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Q: 2) Evaluate yzdx+ xzdy + xydz where c is the line segment from (1,1,1) to (3,2, 0).

A: Given: c is a line segment joining 1, 1, 1 and 3, 2, 0. To evaluate: ∫cyzdx+xzdy+xydz

Q: 10. If mZTSV= (6x + 17) and mSV = (15x + 13)', find mSUV. %3D T

A: A circle

Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: If θ̂ is a point estimator of θ, prove that MSE(θ̂) = V(θ̂) + (B(θ̂))2

A: We have given that θ̂ is a point estimator of θ. We know that  MSE(θ̂) = E((θ̂ - θ)2 )

Q: Compute L{u_2(t) −u_3(t)}

A: