If A = ze?xVi VxA at the point (2,0,3) is + 2xycosy j+ (x + 2y) k then the valueof

Q: et a =i- 2j + k and b= 2i+j +k. Show that la + b| s lal + b|

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Q: 13 - x² – y? at (3, 2, 0), then If the point (1, 1, k) lies on the tangent plane to the paraboloid z…

A: z=13-x2-y2 Partially differentiating with respect to x, we get zx=0-2x-0=-2x Partially…

Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT> XT. Y

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Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

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Q: Suppose w = 6xy + In(4 + z²) , x = - , Y 3u + 9v, z = cos(8u). Find dw/dv when u = -5, v = -6. dv…

A: *to find:- Partial derivative of w with respect to v, when u = -5 & v = -6

Q: find the general solution of the following 2. X Ux +y Uy +t Ut =xyt %3D

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Q: Find the Wronskian W[y,, y,, yal where Y1=t+ 10, y2= sin(2 f), y3 = cos(2 t). a. 8 t+88 b. -8-t-80

A: Given: y1=t+10 ,y2=sin2t ,y3=cos2t

Q: Use Green's Theorem to evaluate -15/4 O -218/3 O 19/2 [(6y - 9x) dy - (yx - x³) da where C' is shown…

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Q: a) h(x, y, z) = In(z³ – 5x – 3y – 1) | 1 b) h(x,y,z) = z³ – Jx + y

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Q: In(u cos v) and y = usin v. Evaluate and z at the point 2е" In y, x 3D (u, v) = (2, 7/4). Let z = du…

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Q: Prove that u exy)= (x+a)Ly+b) is the exact Solution of the pOE Ux Uy = 4xy ucy) where (a) and (b)…

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Q: Let y1 = 9cos(2x) and y2 = 2cos2 (x) – 2sin? (x). Calculate the Wronskian, W(y1, Y2). Give your…

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Q: iv) if zy = (x)- then zx + Zy = %3D %3D

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Q: (3) Derive ACFS Pk, k = 1,2, ... for the following models. (a) Xt = Z¢ – 02Z¢-2 (b) Xt – 0.3Xț-1 =…

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Q: The equations xcos(u) + 9uy2 + e² + 2 = 0 and 3ye" + 4x²v – 3æcos(2) +1 = 0 are solved for u and v…

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Q: Given: Z WXY = LXZY Prove: (XY)? = WY•ZY

A: Given: In the figure ∠WXY≅∠XZY. To prove: XY2=WY·ZY.

Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

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Q: Consider h(x,y, z) = cos (xy) + eY² + In (xz) at the point P ( 1,0, = 1 Deter-

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Q: Let z(x, y) be the function implicitly defined as the solution to TC -2x + y + z + sin(xyz) = %3D…

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Q: 2) al X,X2 =) y = Xi~ ? ,-,Xn ~lid exporen tíal ( 100 b) Xq, X2,--- Xn~ iid N(44i44)= ビ- ~? i=1 %3D…

A: Solution : a) Given : xi  ~ exp ( 44100 )   ; i = 1,2,3,...,n ∴ θ = 0.44     Y    = ∑1n Xi It is…

Q: 2. A firm produces two goods in pure ompetition & has the pllowing TR & TC functions R= 15Q…

A: In this question, concept of optimization is applied. Optimization Mathematical optimization is the…

Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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Q: E={(r,0,2) : 0< 0< n, 0s zs 1, vzs rs 1}. Compute y²e(x²+y²y³ dv•

A: Here, the given solid E is defined usimg the cylindrical coordinates as follows: E=r,θ,z:0≤θ≤π,…

Q: b) = f ) then prove that x ux + y uy + z uz = 0 u

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Q: 3. Use Green's Theorem to evaluate (y-6y) dr + y + 10y) dy where Cis shown below y (-11) (1-2)

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Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: If y is a solution of y(x)-[(x-1t)»(?)dt = 1, then which of the following is true? (a) y is bounded…

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Q: In the given figure, X > K. Prove that WY> JL. K X Y W

A: Here , we have ∠X&gt;∠K we have to prove that WY&gt;JL

Q: that ulx,y) = 42 Cos 3y is the particulas -3X prove Solution of Uxx+Uyy =0 u cx, 플) =0 where…

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Q: In Exercise 5.8, we derived the fact that 4y1 Y2. 0< yı < 1,0 < y2 < 1, f(y1. y2) = 0. elsewhere.…

A: Compute the marginal density function of y1 using the formula: fy1=∫y2fy1,y2dy2 fy1=∫014y1y2dy2…

Q: 20 Given that the (bx) +(ay) =(ab), where a and b are constants. Show that-

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Q: Consider the S.mpto lincar rogressic 3:0n m adol Y tX; t U ukon exp(az.) You have the fallow. ng…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: 13- dy + 2xy = y diferansiyel denkleminin genel çözümü aşağıdakilerden hangisidir? -x* +c1 y = e a)…

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Q: 4. Aşağıdaki denklemi y(2)=1 başlangıç koşulu için çözünüz dy (x² + 1 ) + 4xy = x dx

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Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

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Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

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Q: Find the Wronskian of a given set {yı, y2} of solutions of 6. y"3(x21)y- 2y 0, given that W(T) = 0.

A: Given the differential equation and the value of the wronskian at pi as:

Q: Suppose the goind densiy Runction Xanef y i ginen by frxy) = 44 (ス-8) ○ZXC0,○ ス %3D otheraise…

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Q: Given that y1, Y2 be a fundamental set of solution to the D. E. (e*y')' + y' + y = 0, x > 0 If the…

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Q: x'y=x'+ xy. linear DE Which value of k, the given DE will be homogenous?

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Q: (2,2) b) Evaluate o x*y dx + x dy, shown in adjacent figure using green's theorem. where c is…

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Q: 2. Let z = sin(xy) + x siny,x=u² + w² and y = uw. 2a. Compute Vz= when u = 0 and w = 1.

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Q: Solve the glven differentlal equation by using an appropriate substitution. The DE Is of the form Y…

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Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

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Q: Find the Wronskian Wly,, y2 Y3], where y, =t+6, Y2= sin(7 t), y3 = cos(7 t). a. -343 t-2058 b. 6…

A: The Wronskian Wy1 y2 y3   is given by,…

Q: Find a general solution to (x' +xy')y' = y implict form F(x, y)= C : Give an

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Q: 3 Find the bounded Solution of : = xt メ>。,t>。 >y(メノ) where y cx, o) = %3D and y co,t) = 0 . Ansi] y=…

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Q: 2 I| ysin(xy)dydx Н.W.

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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.