1 Finel a formal solohon to the inihal- bundary value problem. Uflx, t)=6use (x; t) ,oexo Oe x

Q: If 1 =- V(x2 + y²) [(xyz – 3xy)a, + (zy² + 3x² )a, + xy az] And B = r² a, + sin 0 aø Find JÃ x B| at…

A: At P1, 2, 3, A→=25ax+195ay+25az. As r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx, at the given point we…

Q: 4. [cos(2y) - 3x2y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0

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Q: 1y (5x- 8)* + Sin(tan2x)

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate L{u(tπ/2) cos 2(t- π/2)} Option 1 Option 3 se πs/2 8² 2 3e-s $²9 O Option 2 O Option 4 3es…

A: Here we have to find the laplace transformation of the given function.

Q: + sin? x sec? xdx, 1.

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: 1) [ (2t – 1)² dt 2) dx 3) [, x(x² + 1)° dx

A: To evaluate the given integral.

Q: 1. Classify the D.E. 2xe dx + (x²e + 1)dy 0.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 4. Evaluate + tyt - 1j+t sin at k) dt

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Q: Question 11) Find I = CW 1 z- 를 흘리고, 12-1 = secup), 플<<풀,ccw -dz, c:|z-1|

A: We use Cauchy's Residue theorem to solve given integrand.

Q: Beta Function dx 3) Evaluare ta) "(4 – u)". du, (h) Ans. (a) 12л. (h) п 3x -x

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Q: Given equation is dy - sin(x + y) dx

A: Given equation is: dydx=sin(x+y)Let x+y=t⇒1+dydx=dtdx⇒1+sin(x+y)=dtdx Put x+y=t, we…

Q: y = cie“ sin x + c2e“ cos x y" + 2y' + 2y = 0 O y" - 2y' + 3y = 0 O y" - 2y' + 2y = 0 O y" + 2y' +…

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Q: Find o"(x + In y) dydr

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Q: Ex. 14. Find Lt (cos Vr+1- cos Vx) x- 00

A: Introduction :

Q: Jo So cos(y)esin(y)-4xdydx 1-

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Q: 2. (Cauchy-Riemann's equations, analyticity and harmonic functions) (a) Define the symbols Of/0E and…

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Q: F = X 1 + y (tany) j x² + y² = 1 →X Greens theorem

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Q: Question 5 Find the partial derivative for the function z = cos 08--17y¹8sin(x¹7+y¹7) - 17y¹6…

A: Given that     z = cosx17+y17      we have to evaluate partial derivative ∂z∂y .    since we…

Q: 1 8. When we say that (Inx) = , we really mean to con- dx 1 on the restricted domain (0, 0). sider…

A: Given the function ln(x) Now for the derivative : ddx(ln x)=1x Here we take the function 1x on the…

Q: 4) Find ôw/ ôr if w= x=r-s, y= cos(r + s), z = sin(r + s) at the point (r,s)= (1,–1) Ans. 12

A: Find partial derivative using chain rule then put values of x ,y,z in obtained expression then put…

Q: Question 6 What is the (A) ℗ B O D af dy of f(x, y) = tan (x²y³ + 2xy)? 2 [sec ² (x²y³ + 2xy] (3x²y²…

A: Given, f(x,y)= tan(x2y3+2xy)   Formula: ∂∂xtanx = sec2x

Q: Evaluate y = 4x 2 = [{(x² + 2y)dx + xy. dy} from 0(0, 0)to B(2, 4) along the curve

A: Given the integral is :                                  We have to evaluate the integral from…

Q: 3. Find an equation of the form y = ab* + c sin (“x) that fits the data below x | 0 1 | 2 |y | 4 |…

A: To find the equation of the form y=abx+csin(π2x) which fits the data  x0123y4111629

Q: Question 2. Find and classify the singular points of the DE as regular or irregular. (4 Points). а)…

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Q: If x = t2- 2t+1 and y=t²-2t then stationary point is O None of these O (-4,-1) O (0,1) O (0, -1) О…

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Q: 1) [ (2t–1)² dt 2 2 2) dx X 3) [ , x(x² + 1)° d.

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Q: 1 4) S(x, y) = Ans. f(0,0) = -1 local max. x+y -1

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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.