Integrate: [ z²(4x³ – 4) ªdx + C

Q: Findtheintersectionof2x+2y+z=4andx+2y+3z

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Q: (4,5,-3) and b = −i +2j+ k → COMPUTE: 3. bxa a·b

A: Given that, a=4, 5, -3 and b=-i+2j+k We have to find the value of b×aa·b.

Q: Find df (82 + 6y) dA where Dis depicted below. D Q

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Q: Compute A?x and A3x the correct way: ´1 0 () 0 1 A = 3 0 2 0 1 1 1

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Q: The real part of csch(1 + j2) is _____.

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Q: Find an integer coefficient cubic that has x = 1 and x = 2+ /3 as zeros.

A: Given: The two zeros of a cubic polynomial are x=1 and x=2+3.

Q: For the numbers 12, 13, 15, 17, 20 Compute: SX   SX2   (SX) 2

A: Given data is12, 13, 15, 17 , 20

Q: Find the product D (xD – 3) A) xD²– 2D B xD²+4D (c) xD² – 3D D xD²+3D

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Q: Calculate (x+y+z) ds

A: In this question, we evaluate the surface integral for the given intersection of the curves.

Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: In real analysis,Prove that if A is countable, then m(A) =0.

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Q: j) x(x+2)+

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Q: 2. d-4 d+9 2d a²+3d-28

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Q: Evalute ) (2xty)dA, where D=2C2-1にと」 225y41tX)

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Q: Draw the bifurcation diagram for à = (x + 1)(x² – 2.x +r).

A: We are given : Now, the bifurcation diagram for this is :

Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

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Q: Calculate the triple product ā · (b x c), where ā =,b=, and č=.

A: Given vectors  a→=2 , -4 , 1b→=0 , 3 , -1c→=5 , -3 , 3

Q: -) Evaluate 4x2 - 10xy + 3y² for x 2 and y = -1

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Q: find the general salution of ly-3y12)de = xdy,

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Q: /| (9x + y – 2z) dS. Is Evaluate S: z = x + 0 < x< 4, 0 <y< 7

A: Given: ∫∫S9x+y-2zdSS:z=x+y2, 0≤x≤4, 0≤y≤7

Q: Find the inditial equation for xヴ X 9+2Xy+3yso

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Q: Evaluate [ T 1-x² x² + y² dydx.

A: Given: The integral is ∫022∫x1-x2x2+y2dydx. The aim is to evaluate the given integral. Concept:  The…

Q: Evaluate dxdy √√3x + 4y over the rectangle [0,3] × [0,4].

A: We find required integral by using Fubinis method.

Q: Evaluate [1+(x- 1)2 +4y²]dydx

A: Given: The given integral is ∫03∫021+x-12+4y2dydx. Integrate the integral with respect to y.…

Q: For the numbers 1, 2, 4, 6, 8 Compute:  SX   SX2   (SX) 2

A: Given data is1, 2, 4, 6, 8

Q: 1 √x y³+1 2 Sőt. S²/E 0 dydx

A: We are given an integral. Our aim is to evaluate the integral ∫04∫x21y3+1dydx.

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: Use the Cayley - Hamilton theorem to calculate 3 -2 -1 A-1 and A4 if A = 3 4 -2

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Q: If l2 = 3 compute DI, and D = -1 -2 and I2D.

A: Given- I2=1001 and D=23-1-2. To compute- The value of the expression DI2 and I2D.

Q: A chemist creates 200 milliliters of a 52.5 % alcohol solution by combining a 30 % alcohol solution…

A: Here, 30% of the solution is represented by x and 75 % of solution is represented by y. Now, the…