3. Let x? + y² + z² = ? 3ryz, then which of the following is %3D 2y–3zy O a. 2z-3zy 3zy–2y O b. 2z-3zy 2z–3zy Oc. 3yz–21 O d. 22-3yz 2z–3zy 3yz-2z е. 2z–3zy

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: If z = x + iy, z/3 – a – ib and * = 2 (a' -b'), then a is equal а b y to

A:

Q: 3. Which of the following is the same as [(z-2)(3z+5)dz? A) [(z-2)dz + [(3z+5)dz B) [ ziz-2fdz+3[zdz…

A: ∫(z-2)(3z+5)dz ∫ (3z2 +5z -6z -10)dz ∫ 3z2dz  - ∫zdz -∫10dz option C is same as given so answer C is…

Q: Find y dy S using the substitution +5=√√y+2 √y+2 (√3+2-5) (5√y+2+y+21) +C 3 (√x+2-5) (5√3+2-y+24) +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: Which of the following windows will show all 6 points listed in the table? O A. Xmin: -5 Xmax: 8 Y…

A:

Q: Let z = r'y- ry2, r = e 4,y = e2*, then which of the following is az O a. 2e 2t 2e2t O b. 0 Oc. 2e2t…

A:

Q: Calculate fryr if Ar.y,z) = &r-9*y³-z³. OA foe =-322 OB fye =0 OC None of these OD fye = 3r2-3y2-322…

A: We have to find the partial differentiation of the function with respect to X y and z

Q: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

A:

Q: If p (E1) = 0.3, p (E2) = 0.4 p(E1/E2)=0.5 so p(E1 cross E2)= 0.2 0.15 0.12 0.7 %3D %3D

A: Given, pE1=0.3pE2=0.4pE1E2=0.5

Q: dw If w = e+s9, r = uv, s = u + 2v, find di %3D O A. w(rv + 2s) O B. 2w(rv + s) O C. -2w(rv + S) O…

A:

Q: dy Find if y= e©o0s4z dz 4sin4x. ecos4z None -4sin4x. e³in4z -4sin4x. ecos4z

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: If W (2t – 1, y (t), 4t – 7) = -20, then y (t) = O f +5 O ² +3 O 2 - 5 O ² – 3

A: We will solve this by calculate  wronskian

Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

A:

Q: If y" – 6y' + 9y = 0, y1 = e3x, y2 = xe3x = 3 and y'(0) = 12 then find c1 and c2 %3! (а) C1 = 5, c2…

A: We have to find constant

Q: If z = xye», x = u · 3“, and y = u · v², find dz when u ди 2 and v = 5.

A:

Q: If z=x²sinh then дхду O A. (-x³– 3x²y+2xy² – 32x) / 16+x²- 2xy + y² (16+x²-2xy + y²) ² O B. (x³–…

A: Given  z = x2 sinh-1x-y4 We have to find  ∂2z∂x∂y.

Q: (b) If z =W, show that: x- y xy 0 =

A:

Q: Show that A Yk= V' Yk+r

A:

Q: Let z? + y? + 2² = 3zyz, then which of the following is ? O a. 2-3ay O b. 2y Szy 2-Sry Szy 2y 2-Szy…

A: Find the partial differential of z and x then divide by them.

Q: For S(y + 2) /2 –- 3y dy,y = O y = u^(1/3) O y = u^3 O y = u None of the choices

A:

Q: If z=x²sinh then %3D дхду O A. (-x3– 3x2y +2xy2 – 32x)/16+x²– 2xy + y2 (16+x2- 2xy +y?) ² O B. (x3–…

A:

Q: If w = e-s), r = uv, s = u + 2v, find du %3D O A. 2w(rv - s) O B. -2w(rv + + s) O C. w(rv + 2s) O D.…

A: Given: w=e-(r2+s2) ; r=uv ; s=u+2vWe need to find ∂w∂u

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: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: Which of the following windows will show all 6 points listed in the table? O A. Xmin: -8 Xmax: 9 Y…

A:

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: [SADT15] If A (x, y, z) = 2yzî – x²y} + xzrkd o (x, y, z) = 2æ²yzwhat is (A · V) %3D 8xy?z4 – 2x*yz³…

A: Ax, y, z = 2yz i^ - x2 y j^ +xz2 k^,andϕx, y, z =2x2 y z3

Q: If A (x, y, z) = 2yzî – x²y} + xz²k and o (x, y, z) = 2x²yz³, what is (A · V) ø? - O 8æy?z4 – 2a*yz³…

A: I am solving this in step 2.

Q: Let z x²y – xy², x = e-24, y = e2t, then which of the following is a. 2et + 2e 2t O b. –2e2t – 2e-2t…

A:

Q: 1-if M(x,y) =( 2x² + 6xy – y²) then -- and By N(x,y) =( 3x² – 2xy+ y²) then ax (a) 6x-2y (b)-6x…

A:

Q: Given: (2x +3y- 2) - ryz = 0 Evaluate: az (3(2x13y z) yE) y(21 3y z) O (2(211 3y2)+z2) ry (2r1 3y z)…

A: The partial derivative of a function can be calculated when all the variables except the variable…

Q: dz 4. Let r - y – 23 = 6ryz, then the value of is dr %3D 22 + 2ry (d) 코- 2yz 2 + 2yz y? – 21z (c) 22…

A: We are given: x3 -y3-z3=6xyz we need to find the derivative of z with respect to x. This can be done…

Q: If W = 2x 2 + 3xy2 - 20y-2+ 6u; where x = 5u2 +4v 2 and y= u - 4v3 , find §W / §V.

A:

Q: 15. In AXYZ, if ZX = Z , XY = 13r - 21, YZ = 8r – 6, and XZ = x + 4, find x and the measure of each…

A: Solve 15

Q: dw If w(x,y,z) = xe % and x= -4t, y = 4-1, z = -4 + 4t. Find di . (4-1) (4+4) 41(4 - t) -4 + 4 (-4 +…

A: Given, wx, y, z = xeyz     and x = -4t   y =4-t z = -4 +4t We have to find dwdt

Q: 2- find aw dw if w = xy + ду +3/1

A: Given is the function w=xy+eyy2+1. We need to find ∂w∂y. In order to find the partial derivative…

Q: Let z? + y? + z² = 3zyz, then which of the following is ? 2z-3zy O a. 3yz-2z 2y 3zy Ob. 2z-3zy 3zy…

A:

Q: If W (2t - 1, y(t), 4t -7) = -20, then y (t) = O e +5 none O2-5 O 2 + 3

A: Wronskian of two or more than two function is used to chect the functions are linearly inedependent…

Q: Let z = a?y – ry?, x = e 4, y = e2t, then which of the following is 2e2t + 2e 2t a. O b. -2e2t – 2e…

A:

Q: If MZTUV = (9x + 1)°, m<TUW = (7x - 9)°, and mzWUV = (5x - 11)°, find the value of x %3D T W U V

A:

Q: An expression that allows to calculate: 3ry |dr + + 5xy ) dy 4 3 Corresponds to: A) » LL- B) (-r²y+…

A: To solve this problem we shall use the Green's theorem. Green's theorem: Let C be a positive…

Q: Let C: |z – i| = 3 and I = $. dz. Then e 6z z2

A: By using Cauchy integral's formula for nth derivative.

Q: Write equation for each ellipse

A:

Q: 5. Find fx, fy, and fz given x®y? f(x, у, 2) z4 %3D

A:

Q: az ? Let z? + y2 + z? = 3xyz, then which of the following is 2z-3zy O a. 3yz-21 2y-3ry O b. 2z-3ry…

A:

Q: дх and if ry + y2³ + zr' = 7 ду дх Find дт

A: We have to find the partial derivatives w.r.t x and y.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.