L? + y) da + (x + y?) dy ; C: AB, A = [1,3] → B = [3, 0] C: AB , A = [1, 3] → B = [3,0]

Q: M. y dV, where E- {(x, y. 2) | 0 x* 3, 0 yx, - yEs+y}

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: Evaluate ff, x² In(y + 1) dA where R = [0,1] x [0,1].

A:

Q: Using the substitution z=Vx+2, the integral xyx+2 dr is equivalent to (A) | 222(z2- 2) dz .7 (в |…

A:

Q: Given f(x, y, z) = 22 + 2y? + 6z2, find fa(x, y, z) = fy(x, y, z) = f:(x, y, 2) =

A: Solved below

Q: dA, R = {(x, y) : 0 < y< 1,0 < x < 2VI} xe

A: As per the question, we will be evaluating the integral ∫01 ∫02y xe-y2dx dy. So,…

Q: 2 13 y+y+y%3Dx"+4X+12%

A:

Q: -R show that D-2D-31 =0 and hence find D", (b) Given that D %3D

A: inverse of matrix

Q: dy Use separation of variables to find the general solution to dr + 4xy? = 0. %3D

A: We have to sine given differential equation using seperation of variables

Q: If WZ = 68 and UV = 94, what is XY? %3D V W Y U Z

A: Given ,  WZ = 68 , UV = 94  We have to find XY

Q: (c) S, y*/1- y² dy

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Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

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Q: Express ow/ds in terms of r and s if w = x² + y², x=r-S, y=r+s A) 4s B) 4r C) 4sr O O

A:

Q: aw b- if w = x + 2y + z2, x , y r2 + Ins and z = 2r , find the value of ar .rk)

A: We will solve the following

Q: f(z, y) = 2 + + 8y? %3D (x, y)D dy dz , y) = (2, y)

A: Given function is fx,y=2+x2+8y2. Differentiate fx,y=2+x2+8y2 partially with respect to x.…

Q: Sll, dxdydz , where T: 0 < x < 1, 0 < y< v1 – x², Vx² + y² < z< /2 – x² – y²

A: we have to triple integrate using the given limits

Q: Evaluate y ds, C: x = t², y = t, - 1<t < 9 |3D (325)-(5)를 1 12

A:

Q: JJJ Y G inder r2 + v2 = 4y bour inder

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Q: 3) fex,y, z) =5x²y SE C: Pt) = (t°, t,ť> ost«l fdz Sef. FIND

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Q: r In y dr, where D is described by 1 < r < 2, e <y<e aD | V1 +r² dy, where D is described by -1<r<1,…

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Q: Q2) If y(0) = 0 and y'(0) = 0, ƒ (t) = e*t, %3D 1 y(t) = (D + 3)(D + 2)(D + 1)ƒ (t), determine y(t).…

A: Here first calculate differential part.

Q: What is the dimension of {(x, y, z) E R³ : x +y+z = 0}?

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Q: Se xye" dy, C. x- , y-, z- , 0 <te1

A:

Q: i. {(x, y) E R² | y > 0}, ii. {(x, y) E R² | 9x² + y? < 9}, iii. {(r, y) E R² | xy < 1}.

A:

Q: Evaluate II, (z*y +) dz dz dy, where D = [0, 1] × [0, 1] × [1, 2]. %3D

A: Here we have to find the integration if triple integrate: ∭x2y+1zdzdxdywhere D=0,1×0,1×1,2Thus it…

Q: -号。 - 4X u (x,o) =3 e 2 , ニ0 y2 Ansl ux,y) = 34(メ+) Ans.l ucx,y) 3 e %3D

A:

Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: 27. || x sec?y dA, R={(x, y) | 0 < x< 2,0 < y< /4} R 28. || (y + xy-2) dA, R={(x, y) | 0< x < 2, 1 <…

A:

Q: Given f(æ, y, z) = 6x² + 3y² + 4z², find f-(x, y, z) = | fy(x, y, 2) = | f:(x, y, z) =

A:

Q: 1 If Y = x? dy = ? then dz · +c O 22? O 2x 2 dy If y = 6x + 2.5x² + 7x + 2 then dr

A: 1. Given y = x2 So dydx = ddx(x2) = 2x Answer: 2x

Q: af Find y dy √y+2 using the substitution u +5=√√y+2.

A: Follow the procedure given below.

Q: If z = x + y, x = 2t, y = 3t, then %3D %3D 1 5 II

A: Recall:    If f(t) and g(t) are two function of 't' and h(t)=f(t)+g(t) then…

Q: R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

A: If y = a+bx is the linear equation  Correlation attempts to measure the strength of the relationship…

Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Given f(x, y) = – 5x + 6xy° + 3y, find - fa(z, y) = %3D f,(z, y) = !!

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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: (b) dr(x -y) dy, where y, = Va? – x?

A: Multiple integrals

Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

A:

Q: - a. ARWZ W WZ RW b. ? ZR %3D c. RW = 15, ZR = 10, and SZ = 8. WZ 2 and RS = ? R

A: Given, ∠WRZ=∠WZS

Q: d. VxVy, Q(x + 1,y/2) e. 3xVy3z, P(x,y,z)-4 > 0

A:

Q: BD = 10, GF = y, AC = 4, AF = X %3D %3D y D

A: From the given figure BD=GE And Chord of equal length are equidistant from centre  Therefore, AF =…

Q: H = 2 = 0, n2 = 22 and n, 18, thus df is: %3D %3D

A:

Q: I, y ds S:Z=X 0くxく」 こ>Rつo

A: Solve the following

Q: • Given f(x, y, 2) = x³y? + x³z + y?z, find frz. %3D a. fr: = x³ + 2y²z b. frz = 3x?y? + 3x?z %3| c.…

A:

Q: Given f(x, y, z) = 4x2 + 2y? + 6z?, find %3D fa(x, y, z) = fy(x, y, z) = f:(x, y, z) =

A: To find fx(x,  y,  z) =........... fy(x,  y,  z) = ...........  fz(x,  y,  z) =............

Q: dy 16x 9. If r? + y² = 8 then show that dr?

A:

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

A:

Q: O eiz dz < z2 – i e2 , 3 - z(t) = 2e", t e [0,27]. true False

A: