Show that the following statement is false. Vw, x, y, z € R, (w < x) ^ (y < z) → w + y < x + z.

Q: A clamped cubic spline S(x) on interval [0, 2] is defined by 1+ax + bx2 – 2x³ 0<x<1 1+ c(x – 1) –…

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Q: Let f(x, y) = xcosy- y'e*y. fry at (1,0)is equal to: %3D | -2/3 -2 1

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Q: Prove that flx)= (i+x)? + X and diverge Litx)? both

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Q: Find the partial denva tive of in terms 아 y. (z= y tan" (xz)) ay dz

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Q: Transform the BVP 0<x<1 u (0, t) =t u(1, t) = 1 into new one with homogenous boundary conditions, we…

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Q: Evaluate S S f3zdV where E is the solid enclosed by z = 1 and z = x2 +y?

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Q: Let A = { (x,y)e RXR; 0<max{}x-31. ly-21)<1}, then: %3D None of the choices OA is not compact…

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Q: pプ PG2-2(6x)さ子エ theorem over the elosed hemispher defined bY Zz J25-x²_y?

A: Given that F→=x2+yi^-zyj^+z2k^ and z=25-x2-y2

Q: If f: (a,b]-R has a local minimum at pe (a,b) and f is differentiable at p, then prove that f'(p) =…

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Q: Show that(i × j) × j = i × (j × j)Conclude that the Associative Law does not hold for cross…

A: Using the cross products of the unit vectors i,j, k, we obtain

Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: - H.w oprove thaA Scz) = 2is continuous at z=zo O prove that Z if 斗乙キ2。 is dis continnity at Z=Zo,…

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Q: Evaluate the integral ∫c(2x-y)dx+(x+7y)dy along the path C, defined as y=9-x2 from (0,9) to (3,0)

A: Given ∫c2x-ydx+x+7ydy  where y=9-x2  from 0,9 to 3,0 Parametrize C by xt,yt=t,9-t2 and 0≤t≤3

Q: Use boundary conditions (2) in u (x, 1) = X (t) T (1) are, u (0, t) = X (0) T (t)=0 And u (L, t) = X…

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Q: Let Use Euler's Method with h=.5 ond (X,Y.) -(1,1) to estimate (a, y )

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Q: Suppose that X P(X < 3Y). unif(-2, 2) and Y ~ unif(-1,2) are independent continuous RVs. Find P (|X…

A: Given: X ~ U (-2, 2) Y ~ U (-1, 2) X and Y are independent.

Q: let w- f(xy) and y in Poluy Cordeinate then a+yS %3D or or or 7.

A: Given that, w=fx, y And x and y is in polar form that is, x=rcosθy=rsinθ

Q: Let X,Y,T be dotined poinds. Show that if Te X Ÿ then XY = %3D

A: It is given that on considering that let X,Y,T be the distinct points The objective is to show that…

Q: 2. In A ABC, X is the centroid. A A If CW = 15, find cx and XW. W, B. If BX = 8, find BY and XY.

A: we know that  centroid is located 23 of the distance from the vertex along the segment that connects…

Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

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Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to: %3D 1

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Q: Suppose that X1,..., X, are i.i.d with density 1 f(x) = e æ > 0, A> 0.

A: Given:- Suppose that x1,X2,.........Xn  are iid with density  f(x)=1λe-xλ ,    x≥0

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

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Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy

A: Consider a multivariable function . Then the derivative of the function with respect to x is the…

Q: 7.* Give the candidates to local extrema (maximum or minimum) of f(r, y, z) = 2z – y – r under the…

A: The solution to the given question is as follows.

Q: Show that if f(x, y) is homogeneous of degree n, then                                     xfx(x, y)…

A: It is given that fx,y is homogeneous of degree n,

Q: Solve the problem with Neumann boundary conditions, Ut – Uzz = 0, x,t > 0| u(x,0) = f(x) и, (0, t) —…

A: As given by the question There are given that the equation: ut-uxx=0, x, t&gt;tux, 0=fxux0, t=0 And,…

Q: For the qutegradsSEddy tringle Over the bounded by -0,4=0 and *+y=l-

A: We have to find the integral  ∬e2x+3y dx dy   over the region R bounded by curves: x=0, y=0, x+y=1

Q: Suppose that u € C² (R²) and u(x, y) = 0 everywhere on the boundary of the square ((x,y): 0≤x≤ R,0 ≤…

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Q: If f(x, y, z) = In(x7 + yº + z®) + (x° + yº + z®), then find fr, fy and fz at (1, 1, 1).

A: →fx=∂f∂x, During derivative of ∂f∂x, consider 'y' and 'z' as a constant→fy=∂f∂y, During derivative…

Q: Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

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Q: For the Ordinary DE y = f (x, y) to be guaranteed to have a unique solution containing the point…

A: We have to choose correct option where differential equation have unique solution

Q: Since z = In (x2 + y2), x = eucosv, y = eusinv əz/ðu =? az/dv =?

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Q: 0,tor o function frxyuppose that ond fy which is true lor the points Pll,D ond Qc1,2) where Pond…

A: Define D(x,y)=fxx(x,y)fyy(x,y)-[fxy(x,y)]2                                  =x2y2-22…

Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

Q: (3) +. R Ris bounded by the semicircle y = V2x – x² and the line y = x

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Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to:

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Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x&gt;0       =0.000004e-0.02xx2,…

Q: If X and Y are two independent RVs with f (x) = e*U(x) and f „(y) = e U(y) and Z = (X – Y)U (X – Y),…

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Q: . Given: WZ 1 ZY; WX 1 XY; WX = YZ Prove: Wz || XY Y W

A: Since, we have been given that WZ ⊥ ZY , WX ⊥ XY and WX ≅ XYOur Aim is to prove that WZ  ∥ XY

Q: Let f(z) = u(x, y)+iv(x, y) be entire such that u(x, y) = 4v(x, y). Show that f'(z)=0

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Q: {x} € 1, Show that property (3) of a matroid implies: For any S e there exists y € S, such that S \…

A: Following is the definition of a matroid. A finite matroid M is a pair (E,?), where E is a finite…

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: flz) = Im z is continuous %3D

A: The objective is to check f(z) =Im Z is continuous Or not.

Q: If f:[a, b] →R has a local minimum at p E (a, b) and f is differentiable at p, then prove that f'(p)…

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Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

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Q: Evaluate f(x, y, z) ds. Js f(x, y, z) = x2 + y2 + z2 S: x + y = 36, 0 SxS 6, OszS X %3D !3!

A: To evaluate:

Q: Use Green's theorem to evaluate f (x²y) dx + y²dy here C is close path formed y = x and y = x³ from…

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