x2 x 1 Show that y y 1 (y – z) (x – y) (x – z). 2 z 1

Q: (6) y" +16y = g(t), y(0)=0, y (0)=1, %3D g(t) = { 1, 0<t< T 0, %3D

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Q: 1.0 1,0 -1 =) 5f(x) dr = %3D =) L 5f(x) dr =| =) S* 5f(x) dr =| ) | 5f(x)| dx =|

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Q: (x'(t) + 2y'(t) – x(t) = 3 {x(t) – 2y(t) +z(t) = -1 ,x(0) = 0,x'(0) = 1, y(0) = 1, z(0) = 1. Find…

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Q: 5x + 2 Let z(r) = Algebraically determine z-(x). %3D 4.x-3

A: The function zx=5x+24x-3. We have to determine z-1x.

Q: y = In(x vx? + 1) ; find y' x2+1 2x2+1 y' = y' = %3D x (x2 - 1) (x2+1) O Option 3 O Option 2 2x2+1…

A: The given function,  y=lnxx2+1

Q: lim (1, y)→(0, 0) (r + y +9)e-1/(z²+v²)

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Q: X - X (r-F (x-X\r-F) X (x –x) |Y Y-Y 2 1 4 3 4 Compute: X = %3D %3D E(X- X(Y -Y) _ %3D N- 1 B = 2.…

A: x x-x (x-x)2 y y-y (y-y)2 (x-x)(y-y) 0 -2 4 2 -2 4 4 1 -1 1 2 -2 4 2 2 0 0 4 0 0 0 3 1 1 6 2…

Q: (x − 1)y" + y' = 0 — a. y = a 11 αι n=1 + a, Σ + ao η b.y = a Σ=1=xn χη χη η c. y = a 1 + αı Σ=1…

A: We have given a differential equation ,  x - 1y'' + y' = 0 We need to power series solution of given…

Q: f(x, y) = 2x -y-e-* = 0 g(x, y) = -x +2y-e-y = 0 a) For X₁ = 1 and fx(x₁, y₁) = fy(x₁, y₁) = 9x(x₁,…

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Q: 4 P = 80x-2x²-xy-3y² +100y + X(12-X-Y) FinD Px, Pxx, Py, Pyy, Pxy = Pyx, fino x And y Fine Fine P

A: Here's the solution.... please have a look at it...

Q: In Exercises 5-8, calculate the gradient.

A: Here given as

Q: 3. x = 1-5t and y -t+ 3 for 2 < t<6 %3D y (x,y) Domain:

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Q: 1 + (»*/x*)\ x² ) x + y 2.xy %3D (x + y) (x²+y²) + y(2y) y² - x %3D дудх (x² + y*) dz 1 %3D ду 1 +…

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Q: y z lim (x,y,z)>(0,0,0) x² +4y² +9z .2

A: Given limit, limx,y,z→0,0,0yzx2+4y2+9z2

Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: If f (x, y) = V3+ y³ In (x² + y³)ešin(zy+y*) + x² + 10y.then fz (1,0) = %3D

A: We need to differentiate the given function partially w.r.t x. The given function is: f(x,y)=x3+y33…

Q: (1) E(x, -x)² =Ex} – nx² | (ii) E(x, –x)(y; -y)=Lx,y, – nxy (üi) E(x, – x)(y, – F) =Ex,(v, - )

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Q: j x+x2+x+2dx **+3x²+2 lax of S x²+1 of (x²+1)(x²+2) 01 +1 -1 of x²+2 (x-1)dx (x²+1)(x²+2)

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Q: %3D iv) if zy = (x)-1 then zx + Zy = h.x + y c.-z (x + y) d. z² (x – y)

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Q: 2. f(x,y) = In(x+y+3) %3D

A: Topic = Functions

Q: 37. y+ x2 = y* – 2x at (-2, 1) and (-2, –1) %3D 38. (x² + y) ² = (x – y)? at (1, 0) and (1, – 1) %3D…

A: A) given curve, y2+x2=y4-2x  at -2,1 and -2,-1B) given curve,y2+x22=x-y2  at 1,0 and 1,-1.we have to…

Q: +x 5) Let z = f(x² – y²). Show that y ду əx az

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Q: (a). f(x,y)= ln(2xy-11), 1 (b). f(x,y)=- √√16-x² - y² (c). f(x,y)=√√9-x²-y².

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Q: 2 2x Let I = [[ (x² +y°)dycbe . Then I=

A: We will integrate the function and then put the values

Q: 2Fs1 ² f (x, y) dx² proof. (H-w-) 2 ./ = P√= f (gy) - P²Fs (Psy) ар(х,у) 0 as x If f (x,y) → 2

A: Introduction: A Fourier transform (FT) is a mathematical transformation that decomposes capabilities…

Q: %3D iv) if zy = (x)-1 then z, + Zy = b.x+y c.-z (x+ y) d.z² (x- y) a.x-y

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Q: t2 +1 1 2t2 – t – 1 - (ш) f(t) = 1+ - 2t2 – t – 1'V t' x² + 1 - Væ + y +1 (IV) f (x, y) ,x In (y² –…

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Q: 2. x =1+y², x = 0, y = 1, y = 2 about the x – axis.

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Q: х+ у+ z%3 0 х+ у—аz %3D 0 az = 0 —ах + у+ z %3D 0 z = 0 —х + аy — z %3D 0

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Q: x-4y lim (x, y)-(0,0) 6y+7x 3 A O 7 .BO 0.c O does not exist. .D O H/7

A: The limit exists only if the value of the limit taken along any path is equal to a fixed value.

Q: Discuss the continuity of the functions f and g. Explain any differences

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Q: %3D iv) if zy = (x)- then zz + Zy = %3D 2

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Q: h = 0, k 0 and r 8 %3D %3D (x - h)2 + (y- k)2 = r2 x2 + y2 +Dx +Ey + F = 0 %3D

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Q: 1 Q4- If you have 1 then x ... And y = %3D x+iy 1+2i

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Q: (x² +y²) aw W=tan1- (x+y) then ду x²-2x² y²+y² A) (x+y)2+(x2+y2)² -x² +2xy+y2 D) x+y)²+(x²y²)²…

A: if w = tan-1 v then dw/dv = 1/(1+v2)

Q: 1 2 Y = -1 x = 3 using a. (x, y) := x'y %3D 2 1 b. (x, y) := æ' Ay, A:= 1 3 -1 -1 2

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Q: ecos a tan(z+ x) 2x – y+ z V4x2 + y – z xyz T T T x + 2y + 3z 3x + 4y – 2z, x + y + z

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Q: Differential Eqautions  a) y'''+2y''-5y'-6y=4e^x

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Q: 2z2 - z+1 3. Evaluate J.E- 1)2(z+1) dz for T below. |

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Q: əz Q3.If Z= f(x,y)=4e* ln(y), and x = ln (u cosv), y = u sin v, use chain rule to find : 2 ди Q4.…

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Q: 1. x"(t) – 4x'(t) + 4x(t) = 4e²* ; x(0) = -1, x'(0) = -4 %3D

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Q: 1. f(x, y) = 1- x - y 2. f(x, y) = xy 3. f(x, y) = Vx² + y² 2

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Q: 3. 1 1 1 SSS √√(x + y -1 -1 -1 (x+y+z)dydxdz

A: Sol:- ∫-11∫-11∫-11x+y+zdydxdz

Q: 2. y" - y = x, y(0) = 1, y'(0) = −2, h = 0.1 from x = 0 to 1.

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Q: ← Z 3 Z (ancosno) z (ansinno) = z (z-a cose) Z-2axwoso ta azsing Z² 2ax cose + a²

A: Introduction: Z-transformed is significant transformation in mathematics. In many fields, it has…

Q: d³r i: dt3 r"(0) = r'(0) = 0 and r(0) = -1. ' %3D sect

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: x=k y=1. kER 2=k x=1+k y=k ,kER z=1+k x=1 kFR

A: we have to find the parametric equation of the line that passes through origin and A(1,0,1).

Q: f(x) %3 хсos x, (0 <х<2л) Zey 2n а, 3 0, а, —0, ь 3D 1-n a.

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Q: (x - 3)y" + ay + (In |a|)y = 0, y(2) = 0, y(2) = 1. %3D

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Q: 15. f(x, y, z) = xy + yz + zx, Po(1,-1, 2),u= 3i + 6j - 2k

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