If i = 5+2, à = x - ỷ and b = j – z , show that a =

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: If f = xi + yj + zk, l7I = r,and i=, then show that grad () =

A: 1. Gradf=(dfdxi^ + dfdyj^ + dfdzk^ )      2.  dxndx = n xn-1 3. r = x2+ y2 +z2

Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

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Q: For yx + 2x + cx = 9 ,m = 3,Find c at (3,1)

A: Given y2x+2x+cx=9 . m=1. We need to find c at (3,1).

Q: If the first line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: The first line is of the form Ax+By+C=0and the second line is of the form Dx+Ey+F=0 As the first…

Q: Show that if (xig)m.u. is re<rz , it is 8\x,r) C Blxirs] for Jx EX.

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Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

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Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

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Q: 0(x. y) y= Vuv , then find 2. If x=, at (1,1) O(u.v)

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Q: If A = and if xy = 1, then det ( AAT) is equal to y a

A: We have, A=axya As we know that, transpose of a matrix is obtained by changing rows to columns and…

Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: If ds dt Vst , and t = 0 and s = %3D 1, find s when t = 9. A. 81 В. 100 С. 121 D. 144

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Q: Q1/ If z = e*?y, x = Vuv, 1 y = Find: əz а- ди az b- dv

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Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

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Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: Given F(x, y, z) = (z, x, y) Solve for: а) divF b) curlF

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Q: 1. If 4=x'zi-2y'?'j+xy'zk , find div4 at points (1, -1,1).

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Q: If z = In /x? + y? , find x- X +y В. 1 С. D. Vx? + y? A.

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Q: Find H(−2) and H'(−2), where H(x) =

A: Here we have;  H(x)=∫-2xduu2+1

Q: for z = In(2® + y*). Find

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Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: If w = x*y+y*z+2x, Verify the following identity: dw dw dw + ax' dy' az = (x + y + 2)²

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Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: If S(x, y)= x² +y , find f, and f, . %3D Vr

A: Fx is partial differentiation of F with respect to x.

Q: If A = *yzi – 2x² j + xz? k and B = 221 + yj – x° k, find za (AXB) at (1,0,–2). Ans. -41 - 8j

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Q: If A = and if xy = 1, then det ( AAT) is equal to y

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Q: Let r,s,t,u be the roots of the equation x* + Ax + Bx + Cx +D = 0. Prove that, if rs = tu, then A D=…

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Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: If XM = 4, XN = 6, and NZ = 9, find XY. %3D %3D %3D 2. If XN 6, XM 2, and XY 10, find NZ. M. %3D %3D…

A: Solution:- The step-by-step solution of the question is given below..

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

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Q: 3 - If h(x, y) = y – xy – x2, find at the point (2, n) ду

A: The given function is hx, y=y-xy-x2 and the point is 2, π.

Q: If h(z) = 2 – 4, find h(z). %3D

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Q: If u=l0g Cx +ytz- 3>yz) prove that Ce+y+z) he

A: Given that u=logx3+y3+z3-3xyz Then  ∂u∂x=3x2-3yzx3+y3+z3-3xyz ∂u∂y=3y2-3xzx3+y3+z3-3xyz…

Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: Derive pz, 192. sjt9z, Hz(t), ez, čr: directly , if X ~ U (0, w) with r = 20, n = 30, w = 100. %3D

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3x + 2u − v + 2w = 0

A: The given vectors are Let the vector x be

Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: Let u = 2i−j+3k, v = 3i+j−k, and w = 3i+j+2k. Verify Equation (3).

A: Given- u=2i-j+3k,v=3i+j-k and w=3i+j+2k To verify- The equation u×v·w=u·v×w

Q: Show that || Ar +b|3 cTx +d f(x) = {x |c"x +d > 0}, where A E RmXn, bE Rm, c€ R" and d e R.

A: As per the instruction, we will be solving part (b) of 3.23. We are given the function…

Q: Suppose that r, y, z satisfy the equations x+y+z = 5-a %3D 2x +y = 7 – a %3D x - y – 2z = 0, %3D…

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Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

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Q: Suppose A = xy" where x, y e R". Show that ||A||2 = ||x||2||y||2-.

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Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.