[x +1 0 2 1 2 (3)if A = 3 1 and B = 3 y -5 4 -1 -5 4 z - 4. Find x,у аnd z.

Q: Let a A = |d e ghi Assuming that det(A) = -7, find (a) det(3A) (b) det(A) (c) det(2A-) -- a (d)…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = 1 + xy2 - 2z2

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Q: If f(x, y) = xe2y + 6xy, then is dydx given by: e2y + 6 등 2e2y + 6 2 O None of these O 2xe2y + 6…

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Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

Q: Use separation of variables to find a product solution to the following: ди ди x==y дх ду u=c X…

A: Solution :

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

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Q: if f(z) = (ax – x³ + 3xy³)+ (by – 3x²y+ y') is anal ytic , then the value of a and is

A: We have , f(z) = ax - x3 + 3xy2 + iby - 3x2y + y3 We have given that ,  f  is analytic function.…

Q: given f (z) = 32² – 6z + j3, what is the value of u(3, 2)

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Q: Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3)…

A: 1) COV(X,Y) =E(XY)-E(X)E(Y)                    = 5-1×3                    = 2

Q: a of the following juncions. s- 1 (b))F(s)% = %3D 2s2 -8 s + 11

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Q: "-y'-12y=x * O y= C1(e^4t) + C2(e^3t) + (t)/12 + 1/144 O y= C1(e^4x) + C2(e^-3x) + (-x)/12 + 1/144…

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Q: 03. Find se and *. If f(x,y) = 2e* + Iny² ,and x = 2t + r2, y = ; %3D at r+1

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

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

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Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: 4. (a) If y = A + Bx + Cx2 and yo, yı, y2 are the values of y corresponding to x = a, a + h, a + 2h…

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Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: f(z) =z2 is discontinuous in C

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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 X =V1-t and y= - 3t +t°, what is y' ? O 6(? – 1) /1- O -3 (t? - 1) /1-t %3D 0-6 (t-1)(t + 1) /1-t…

A: x=1-t and y=-3t+t3

Q: Given: 5x+4y= 24, x + 7y= 11; Prove: y = 1

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Q: Consider f(x, y) = x³ + 2ry + y. Compute the following: (b)

A: Answer and explanation is given below.. Simply do partial derivative with respect to x and y.

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: For æ > 0, 1 dt 1+t2 A 2/7(1+z) B 2/7(1+JE) c) 1+1 D 1+z E VE

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Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: 1. If x, y, z E R, prove that (c) ||x| – |y|| < |x –yl. (d) \xy| < }(x² + y²)

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Q: If z = (2x + 3y)³ and x = r2 - 2s and y = 2s - r, then when r = 2 and s = 1 is as %3D %3D

A: To find the partial derivative when r=2, s=1.

Q: Express In x V in terms of in x, In y, and In z. 2mx-글 my-글 nz 2 Inx + 글 Iny-글 mz znx+my+nz In y 2nx…

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: Verify that u' (t – a) = 8(t – a) by solving the problem x' = 8(t – a); x (0) = 0 to obtain x (1) =…

A: What is Laplace Transformation: Laplace transformation is crucial for control system design. Laplace…

Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: ở =, then If f(x, y, z) = In(2 + x² – 2y² – 3z), Duf(2, –1, 1) = A) % 11 V3 В) 11 C) D) - E) OC O D…

A: The solution is given as

Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: If f (x, y) = V3 + y³ In (z +y°)e*in(zyty") +2² + 10y , then fz (1,0) = |3D %3D O 2 4. O 3

A: Given that fx,y=x3+y33lnx2+y2esinxy+y2+x2+10y3 First we have to find fxx,y where fx=∂f∂x

Q: a) Evaluate ²₁ √√1-x² √√1-x²-y²e-3(x²+y²+z²)² dz dydx

A: The given problem is to evaluate the given triple integral of Cartesian coordinates.

Q: Is the ex (-1,0) (2) (镇) 2) 學 6 GL/Y 180° 7643 5 135°- 50 150° -√2-√2 120° ( OT 210° 225° T 240° y…

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Q: Determine c1 and c2 so that y(x) = c1 e^2x + c2 e^x + 2sin x will satisfy the conditions y(0) = 0…

A: NOTE: Refresh your page if you can't see any equations. . the given solution is…

Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

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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: Q3) If f () = 3y5+2x5+4x2y³ prove the following %3D x²y3 af(x,y) af (x,y) 6(x + y). %3D əx ду

A: Given: fyx,xy=3y5+2x5+4x2y3x2y3

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: Evaluate /, a Te dydx y2 2 JJ4X-x² 32 dydx (x²+y²)' V4x-x? O 4 In(v2 – 1) – 4+7y/2 3 4 In(v2 + 1) –…

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Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

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Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

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

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