1. Compute the following double in- tegrals. a. SSr 2x + 4y + 10xy dA, R : 0 < x < 1,0 < y< 2

Q: Consider the following LP (a) Find the dual of this LP 3x₁ + 4x₂ + x3 x₁ + x₂ + x3 = 50 2x₁ - x₂ +…

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Q: 3. Evaluate || (3y+ 2x“) dA, where R = {(x, y) E R² : |x|+|y| < 1}. R.

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Q: Two students are named to present their work from a class of 12 students: 5 from electrical…

A: Total = 12 students Electrical = 5 students Telecommunication = 4 students  Computer = 3 students

Q: Evaluate the following. √6 / (x - 5y + 2) ds S S: z = 11 - 6x + 8y, 0 ≤ x ≤ 5,0 ≤ y ≤ 1

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Q: Find dy for each of the fo llowing (4) y In (tax? tbx +c )

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Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

Q: Integrate: +C 16t6 t4 [√16 dt

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Q: Prove that fVf · dr = 0.

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Q: 6. Given r + y° = 1, find y"

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Q: 15. Calculate (41 + 3, r?. –4r³)dt.

A: To calculate: ∫034t+3, t2,-4t3dt Solution: Power rule of integration states that: ∫xndx=xn+1n+1…

Q: Differentiate y=In (In 4x) 1 A x In 4x -1 B x In 4x. In 4x D) None of the given choices In 4x E.

A: f(g(h(x)))= f'(g(h(x)))×g'(h(x))×h'(x)here, h(x)=4xg(h(x))=ln(4x)f(g(h(x)))=ln(ln 4x)

Q: 4.) x : 12 required:a) find the value of x if y = 1/2

A: Given, x=-112y142y-y214We need to find value of x when y = 12

Q: 2. If z = x° In 2.xy, find at 1,-

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Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: Use Gramer Rale Find L3,2 -2x + 33-Z-1 3J-2-1 * + 2y-2- 4 -2x -+2 = -3

A: -2x+3y-z=1x+2y-z=4-2x-y+z=-3 Here, D=-2  3 -1  1  2 -1-2 -1    1,  Dx=  1  3 -1  4  2 -1-3 -1    1,…

Q: A Show that : tan" [ ica-a)' (2ta)) -i 2

A: Let ax=eiθ. So: tan-1ix-ax+a=tan-1i1-ax1+ax                         =tan-1i1-eiθ1+eiθ…

Q: x 6. Differentiate: y = x² + 3x - 1 A. C. x²+1 x²+3x-1 -x²+1 (x²+3x-1)² 0 2x²+3 eldet 10-(x²+1) B.…

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Q: Rationalize hxVx+h Vx - Vx+h denominator: |

A: Rationalize denominator  h√x√(x+h)/√x-√(x+h)

Q: 3. For Z= xtanxy,evaluate Zyy

A: The given function Z=x tanxy We have to find Zyy.

Q: 8. Let D be the rectangle given by -1<ys0, 1s x< 3. calculate ff,(x2 + y)dydx

A: 8. We will evaluate the given double integral. Given integral is ∬D(x2+y)dy dx with the limits…

Q: solve by seperating the variabler

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Q: 7.Find a²z of z = 2x³-5xy² xy

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Q: 4. Find dy for y u² eu for y=+* du

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Q: b) Consider the second-order DE. y" +25y = 0 rE (-00, 00) Show the zero’s of the solutions separate…

A: The given differential equation is y''+25y=0 If D=dydx then equation will be D2+25y=0 Now Auxilliary…

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: Let U = x'e . Find dU .

A: The given function is: U=x2eyx Therefore: dU=∂U∂xdx+∂U∂ydy

Q: Set X = x 0 1 Y where x, y are unkonwns. Solve the equation X² = 10

A: given and

Q: For each of the statement below, decide whether it is true or false, and prove your claim. (a) For…

A: Sum , difference, product and division of rational numbers is rational

Q: Based on the following: i: x ≥0 ii: y ≥0 iii: z ≥0 iv: 0.5x + y + 0.2x ≥ 600 v: 2.0x + 3y + z ≤ 2000…

A: Here we have to solve y+0.2z = 600 and 3y+z = 2000 and find the values of y and z. Before that let…

Q: 1. Do not use a theorem to find the ff. Z if yz? + z = 5xy – 1. %3D

A: In the multivariable function, if we have to find the partial derivative of one variable with…

Q: y (5) + y(4) + 18y (3) + 18y(2) +9y(1) +9y=0

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Q: f (て) be a top. space 3.ト X-Tab, cidiel (xて) be top space %3D %3D et A= {bj. FindO A Tb,d] %3D 2.…

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Q: F 6) Frud the weasuves of all six augles of hexaqou MCA= 2X+ら ABz X-10 WCC =X+5 TucD=x u CE = x+1S…

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Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

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Q: Evaluate the following. 5y + z S: z = 15 - 6x + 8y, 0 < x < 1, 0 < y < 3

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