u(t) where u(t) – () a1 and u; (t) = Bie" + Bet and ua(t) = Bze" then 12(t) %3D %3D a2 a. a2 =3 b. ag 2 C. a2=1 O d. ag=-4 3.

Q: T(x,y, z) = x² + 2y² + z

A:

Q: z = x2 + xy4, x = uv? + w°, y = u + ve" dz when u = 3, v = – 2, w = 0 dv then find:

A: Solve by partial differentiation

Q: y"(t) – 4y'(t) + 5y(t) = e"U (t – 2), %3D

A:

Q: J = fc cosh (z) dz, z2-3iz C: |z| = 1

A:

Q: Find the general solution of (D4+ 50D²+625) y=0_ A y=c,cos5x +c,sin5x ® y=c,e*+c,x* +cze-5«.…

A:

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

A:

Q: 2.Evaluate . xy+ds where C is the right half of x2 + y? = 16

A: Integrate with use parametric form

Q: Q4. If y= f (t) and x=f (t) d²y dx2 dy 3 and %D 4t dx2 dy By using chain rule, find dt

A: Chain rule is given by dy/dx=( dy/dt )× (dt/dx)

Q: D = {(x, y) E R² :0<x <∞, 0 < y<∞} olmak üzere, [ rye--v°dA D.

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

A:

Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

A:

Q: Ifx' +y +z -2aņz =1, then show that V1-x dy 1- y V1-:

A: We have to use the given condition x2+y2+z2-2xyz=1 to find this.

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

A:

Q: and v= x2y% if z- fcx,y) where show that dz dv u=X-y 出。是、会 dy 24

A:

Q: Solve the I.V.P: dy = 6y²x; y(1) = 6y?r; %3D dx Oy 1 372-8 1 Oy = 8-3z2 Oy 1 8+3z? Oy = 1 !! 8-3z

A:

Q: Minimize c = r + 2s + 3t 3r + 2s + t > 60 Subject To: 2r + 3t > 60 And Where: {r > 0, s > 0, t > 0}…

A: According to the given information it is required to solve the given problem:

Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: 4) Suppose that T : R³ → R² is defined by T((x, y, z)) = (1+2x – z , 3 – x + 6y) Is T linear?…

A:

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

A:

Q: What is the antiderivative of J (5t° 2t* + t + 3) dt. c.t° -+t + 3t 2 а. t5 +t2 + 3 с. b. t° -t5 +t2…

A:

Q: What is the general solution of zyda - (2 +3y) dy = 0 ? O a + oy In y Cy og In y = C 6y Iny cy? Quiz…

A:

Q: (c) Ã = xẽ, + yếy, C : {n² + y² = 1, z = 0} %3| ex (d) Ā = En + Ey 2 + 12 C : {y = x, z = 0, x € (0,…

A:

Q: dw ,s = 1 If w = 2x? ds + y, x = 2 - s, y = 1+ 2s², then by chain rule when %3D సా | 8

A: See the attachment

Q: af af a²f 1. Given f(x, y) = x' + y* find ax ' dy' dxdy and - дудх

A: Please see the answer below

Q: D'y + GD'y - 54Dy - 8l y =0 A. * + Ca x*e* Ge* + (C2 + C3x + C4x9e¯³× C4 x²) e -3x 3X y = C, "+ Cze*…

A:

Q: + y = e In t 16. 2y" + 2y' + y = 4Vx 17 3x" 6y' + 6y = e* sec r

A:

Q: Q.IB) If w=f(u, v) where u = tan ¹2 &v=ln(x² + y²), the show that: Əw dw aw +y ax dy 2- ду x-

A:

Q: Calculate the LOS of y = x² + 2x + 8 LOS is x = a is b is cis

A:

Q: What is the general solution of the given DE m2y = C,e™1* where C1, m1, m2 are constants dx and m, +…

A:

Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

A:

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

A:

Q: (i) Vx EN By €Z YN Pf W Why? (iv) ar €Z (wsc) vy €N Y N Pf w Why? ax €Z ay ez YN PI W Why?

A:

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

A:

Q: Evaluate using the u-substitution technique. 1. s + 2s ds s² + 1 x³ =dx Vx4 + 9 2. 3. (2y + 3)/y+ 2

A:

Q: Evaluate SSS 2e(a²+y²+z?)"² dV over B where B= {(x,y, z) : x² + y² + z² < 1}. Take n = 3.

A: • The given region B has spherical symmetry, so it will be easy to solve this volume integral in…

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

A:

Q: 2 2xy) dy, v es (0, 0), (2, 0), (

A:

Q: %3D 23. f(x, y, z) = 2x + z? subject to x² + y? + 2z? = 25

A: Lagrange's Multipliers: The Lagrange method is used to maximize or minimize a general function…

Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

A:

Q: ( a) 2.xdV where E = {(x, y,z) |0 < y < 2, 0 <xs/4- y² ,0 < z< y } E

A: As per Bartleby's answering guidelines, we are supposed to answer one question if more than one has…

Q: Let f (x,y) = 9e2*y what is fryx (x, y) =? %3D Select one: Oa. 36xye2*y + 72xy?e2*y b. 72ye2xy…

A:

Q: | 2.xdV where E = {(x, y, z) |0 < y < 2, 0sxs 4- y²,0<z< y}

A:

Q: if y' - y =2x Then, d'y -24y prove that dx (3y –1)

A: Given that: y3-y=2x

Q: (a) The function z depends on u and v so that z = 2v(4- 3u)? u = 2x + 3y and v= 3x-2y az when x 0…

A:

Q: f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

A: Here f is two variable function .To find ∆f , first calculate fxx and fyy then add them.To find fxx…

Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

A:

Q: 3. r/s*t/u- v + w * x - y++

A: Given expression is, rs*tu-v+w*x-y++

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.