how can i derive this equation in 3 D? *be aqy ay az at Əx

Q: 5. Prove that So*(y – 0)dydr =

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Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the integration over the region using the triple integral. First we will find…

Q: 3.) Prove (cA)" = cCA) %3D

A: Let A be a m×n matrix so A=(aij)  1≤i≤m and 1≤j≤n ie A has m rows and n columns. By AT we mean…

Q: 3) Show that the tangent(45°) = 1. Let "u" = 22.5°, use calculator %3D

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Q: 4/ur grans funthon y"-Uy't3y = et

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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: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: 2. If z = x° In 2.xy, find at 1,-

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Q: Prove az - ae that d az dz

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Q: 11. Jlgull sin(2t +) dt %3D e2t-3 4 4. 64e3

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Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

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Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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Q: Find dy ax 9=бл+бай

A: Given :y=x+1+xformula : ddxx=12x

Q: and 3 point Gauss Quadrature 2 By using e sfim afe : 2 dx メ-2 い)S, dx Nx

A: The given problem is to estimate the integral using 2 point gauss quadrature rule and 3 point gauss…

Q: 3. From Eq. (1), deduce that U2n-1 2. U2n 2. %D %3D n 2

A: 3

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

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Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t>0=0, t<0 Therefore,…

Q: S dy 7 y2-8y+5

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Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: Use Greens Theorem to evalute fyx² dx + x²dy as shown below Leh Half of (0,5) +y-25 (0,-5)

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Q: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A: ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: solve the given nonhomogeneous ODE x^2y"-2xy'+2y=x^3sinx by varition of parametrs

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Q: Use linearization to approximate In(1.2).

A: we can use the following formula for approximate calculations: f(x)≈L(x)=f(a)+f′(a)(x−a). where the…

Q: Show that 3x2 +6x +2 = 3 (x+1) - by completing the square. Hence, evaluate the 2 integral dx. V3x? +…

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Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

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: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: 3 1-Vy dy 2 2у3

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: Consider the following BVP: - 2u 1 1sxs2 dx Using boundary condition u(1)-u(2)-0.

A: Sincei have attempted similar problems, let me solve the given problem step by step....

Q: If In(ax)dx = 2, then a = %3D 1

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Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

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Q: If In(ax)dx = 4, then a ( In(ax)dx %3D 1 4

A: we have to find the value of a

Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: Determine the general solution for following Cauchy-Euler Equatio dy + 7x +5y = x³. i) dx2

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Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm & integration formula of sech(x)

Q: Prove that S. 8 dx √π 2

A: This question is related to integration using gamma function.

Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

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Q: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

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Q: Show that lm Casy -1 CoSy-1

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