-x ôx ô -0, ây for z = tg(xy)+. y

Q: Given f(x, y) (8a®y + 3xyf). Compute: dx?

A:

Q: dx -dx is converted to: 4+Vx By algebraic substitution, the integral |- 2ydy A y+4 dy B y+4 ydy © S…

A:

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

A:

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

A: Integrate with use parametric form

Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

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

A:

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: C is given by x = t', y = t', z = t', where t runs from 0 to 1. Evaluate (z dx + xdy + y dz) 33/20

A:

Q: Given f(x, y) 1* + 2xy° + 4y“, find fz(T, y) = fry(1, y) =

A: The given function is f(x,y)=-x3+2xy6+4y4

Q: "III. Vf dr = , where f = xy²z and Cis given by r (t) = (t +1, t², t³),0<t<2

A:

Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

A:

Q: SSS 12z dV E where E is enclosed by z = x? + y² and z = 1 О Зл O 27 O 4T O JT

A:

Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: Given f(x, y) = 1æ²y then the total differential df = %3D

A: I have appended the formula used in the solution part.

Q: Integrate the following using substitution 1) z5 (9z6 – 7)8 dz 2) S dy 4 y3 2-5y4

A: Given that: 1. ∫z5(9z6-7)8dz   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: f(z) dz where a inside r= Z-a 2ni O 2nif(a) O 10

A: Using Cauchy integral Formula:

Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

A:

Q: E(x)三ㄧ-rx.VY.tmdt. Į nd Eicx) Let

A: Since f(t)=sqrt (4-t^2) is even function , so we use the property of definite integral shown on…

Q: i) ais f(x,y) = x2 + 3xy + y -1 Laalic * Te Te

A: Given that  Af(x,y)=x^2+3xy+y-1  To find the partial differentiation of f(x,y)

Q: dy where C is defined by dx + x2 + y? Evaluate x2 + y? C T(t) =,0 <t< 2n

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: Q2: Evaluate o o" y*(x² + y²)dx dy 1 cV1-y? y² (x? + y?)dx dy

A:

Q: If y = e3+, x = 0 when z = 1, z=1 z=1 = 3, then what is z=1? dy |3D O 1 O 3 O 21e4 O e30 O 19e30

A:

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

A:

Q: Find fy, fy, and f, for f(x,y,z) = 4xy + 6xz + 2yz.

A: Given, f(x,y,z)=4xy+6xz+2yz

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: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds…

A:

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

A:

Q: Exl Let c R,Z) be usual toP s Pace and A-fcxy)ER/ x²+y²< 13 find A Ext CA), Ā , A°

A:

Q: س/ أختار قيمة R ,D المناسبة ل لداله الاتية f(x) = 2 + Vx? - 1 Df = {x:xeR:x 0} O الخيار رقم 1 D, =…

A: The given function is fx=2+x2-1. Calculate the domain and range. Range is defined the all possible…

Q: dz where a inside r= C z-a 2ni

A: We have to find integration of given function Using Cauchy's Integral Formula.

Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: : // (x + y – 32) dV where E = {(x, y, z) | 0 < y < 1, 0 < x < y, 0 < z < r + y³} Evaluate - E

A: Triple integration

Q: Find the general solution to dw ol Sa'(t) = x(t) – y(t) + 3e'; ly'(t) = y(t) – x(t) + 2e'; (8) (8)…

A:

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

A:

Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

A:

Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

A: Given, u= ∫dx/(4+√x) We can solve it by substitution method.

Q: f(x, y) = sin(z³ – 7y) %3D

A:

Q: Differentiate. R(t) = (t + e)(2 - VE) %3D R'(t) =

A: Given function is Differentiating both sides with respect to x by using product rule of…

Q: ürkçe: f(x, y) = 4 + x° + y° – 9xy fonksiyonunun yerel ninimum değerini bulunuz.

A: Please refer to the image below

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

A:

Q: F (r, y) = (3x²y² + cos y + ye", 2ar*y - - r sen y + xe*)

A: Given F→x,y=3x2y2+cosy+yexy,2x3y−xsiny+xexy. We have to determine whether the vector is gradient…

Q: sin(r. r dr dy. Compute O y/3

A: To evaluate∫01∫y131sin(πx2)x2 dx dyx= y13y = x3

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.