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Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: If z = e'x + y In(x), find z, and z, Zx Zy II

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

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Q: In ABCD, H is the centroid. If HF=6 find BF. C E

A: It is known that the centroid of a triangle divides the median in 2:1 ratio. It is given that HF=6.…

Q: If AB = B for some B # 0, then A is inertible.

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Q: Let (B; ) be a Brownian motion with Bo = 0. Define a process (Z,) by Z, = B{l/t for t > 0. What is…

A: Given information: It is given that Bt is a Brownian motion with B0 = 0.

Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

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

Q: If e dy then y-

A: We will evaluate the following Integral.

Q: 2 dy y+ 2xy di feransigel deiklenin 2.

A: To solve: The differential equation dydx=y2+2xyx2. Concept used: Power rule of derivative:…

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

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Q: Sow that 2 x² + y² + z² - c²t² is Lorentz invariant.

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Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: 1. Use the Chain Rule to find u and ou for w = x²y3 where x = dw at s2 +t2 and y = ds

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Q: Express aw/ar and ôw/as as functions of r ands using chain rule w = = In(x² + y² + z²), x = res sinr…

A: Given problem is :

Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: HiW f(x, y) = x +2xy+y² +3x+5y ils Is.5 of (2,-3) (2,-3) al of

A: The detailed solution is as follows below:

Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

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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: Eva 6 SSin'z osx dy

A: ∫undu=un+1n+1.     cos2x+sin2x = 1

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: The auxiliary (charasteristic) equation of the DE x²y" + xy' + y = 0 is %3D

A: Euler-Cauchy type differential equation: Let a equation x2y''+y=0 ..(i) Put y=xm in the given…

Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: Evaluate Sm e" dæ. • 2 does not exist (diverges)

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Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

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Q: ди and ди ди Q3. If u = e"" sin p, p= sin x, q = z' In y, r=1/z, use chain rule to find

A: Find your answer below

Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

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: If z = e4x + y In(x), find zx and zy. Zx Zy %3D

A: 1) The given function is: z=e4x+ ln(x)

Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: 21. |'t cosh t dt Jo

A: Note:- These are multiple question and according to our company guideline we can do maximum one…

Q: Fand the anti daniahir of fw. e+e- 2Cosed px -

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Q: terms HK K . J 12 in

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Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: Let {yk } be the DFT of {x; }, where x = [0, –1, 0, 1] y3 = O i -1 -i 1

A: Here, x0=0, x1=−1, x2=0 and x3=1 We have to find y3 Now, y3 is given by…

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: if y ". y (In z) (a) Find

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Q: If f(x) - g(x) = 1, then f and g have the same antiderivative. %3D O True False

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Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

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Q: If s = 3/t + 1, then ds Preview %3D dt

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Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.

Q: Please solve this Differential Equation question. Thank you!

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Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…

Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

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Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

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Q: Show that there exist constants 0 < A < B <∞ such that, for every y, z ER with A В 1 dx < ly – z|3…

A: We need to prove that there exist positive and finite constants A≤B such that, Ay-z13≤∫ℝ1x-y23…

Q: 1. Find the linearization of r – z at a = 2.

A: Find the linearization of x3-x at a=2.

Q: Show that (A − B)T = AT − BT .

A: We have to use the properties of subtraction of matrices and matrix transpose operation. In matrix…

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…

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.