5z-4y 2z+y If z F (z,y) where z sin (u) + cos (v) and y = u + u² + v? evaluate dz where u v = 0. %3D %3D du Enter your answer in the box below. Number

Q: Q1// B: If u+v=e cos y and u-v=e'sin yfind the Jacobain of the a u, v at (x.y) (1,0) dx,y function

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Q: In Exercises 35–40, find the partial derivative of the function with respect to each variable.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re…

Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: Fial dy ldx by imphieit differention. X² (x+y)=y?(7x-y) 2. Find dy /x by implicit differention. e…

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Q: b) Find the potential P(x,y) attached to the exact ODE 2r sin(y) + x* cos (y) y = 0

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Q: Current Attempt in Progress dz Use an appropriate form of the chain rule to find dt 1 y = 7t z = 9…

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Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)=pi/6. 1…

A: We use the concept of exact differential equations to find the general solution to given…

Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x*yt cos(2)) 4,4 fm = fu f2 =

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Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

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Q: 2n X f(p sin()cos(0) p sin ()sin(e) • p cos(o) p'sin (4) f(x, y, z) dV = dp de de Jn/2

A: SPHERICAL COORDINATES : The spherical coordinates are : x=ρsin θcosϕy=ρsin θ sinϕz=ρcosθJ=ρ2sinθ…

Q: 2t Let y=10 In cos(e dy = dt AeBt sin (e2t) Then cos (e2t) where C = D = %3| ABC

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Q: (x+y²); x=e°cosu, y= e'sint at (u,v)= (/3,0). Let T= xy la (x+y²); sinu. ン

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Q: 10. y' + 5xy = 0. y = ce 25 y(0) = T 12. yy' = 4x, y - 4x2 = c (y > 0), y(1) = 4 %3D 14. y' tan x =…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: az and dy Find 1. z = 4e**3 2. z = fir 3. z = cos (x°y^)

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Q: fc (x2+y2+ z2)ds , C:x=t y= cos 2t z= sin 2t, 0 < t < 2pi

A: Given that, C: x=t, y = cos2t,   z=sin2t   and 0<t<2π

Q: Q3) f(x,y)= y'sin(2x)+x²(cos(y')) find fyyxy уууххху Q4) w(x,y)=x siny +x²- (2x²+3y)² find dw

A: It is partial derivative

Q: xy' + y = 0, y(4) = 6 y'cosh?x = sin² y, y(0) = }7 TT y' = -4.x/y, y(2) = 3 xy' = y + 3x* cos²…

A: As per guidelines, I can answer only one question. Since you have asked for multiple questions, so I…

Q: e2 (2 cos y dx – sin y dy) = 0, y(0) = 0 – sin y dy) = 0, У (0) %3D

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Q: ysin2-xcos2x dy = 0 16. x cos + ysin2} y sin r cos Ans. xy cos y = a dx dy y+Vx +y? 17. Ans. y+Vx…

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Q: dz Find when u= 1, v=0 if z= cos(xy) – xsin(y), x= u² + v2, y= uv. dv A) 2 B -1 D) 1 E -2

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Q: dy Os:A- Find for the following functions: - dx 1- 1+secy xy2 = 1+ x* t2 2- If y = and t = V2x + 1…

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

Q: Q.6) Evaluate F. dr ds dy, where F(r, y, x) = 2k and r(x, y) = sinx cosy i + sinx sinyj+ cosr k.

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Q: a) u=r³-3ry² + 2xy + x, D) u= x² - y² +5, c) a= sinh rsing, d) u = e(y cos y + x siny), e)…

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Q: Fu = x? + y? + z?, where x = e2t, y = e2t cos (3t), z du en at t= 0 is - dt

A: In this question, the concept of the derivative is applied. Derivative We can use a derivative to…

Q: dz dz and dv Use an appropriate form of the chain rule to find du z = =; x = 16 cos u, y = 15 sin v…

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Q: Home work 2 find and 35 if w= CX +y +Z)< × ニ と-S yニCos (r+5), そ ニ sin (r+5) ノ aud 5 ニ1

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Q: general solution DE Xy" +y'+xy=o Find the of on co ∞)

A: The given differential equation xy″ + y′ + xy = 0, known as Bessel’s equation of order zero, has the…

Q: 4.1 z+ cos(T2) dz, z(z² + 1) with C: |z – i| =.

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Q: Q5/ Find Vf for f(x, y, z) = e** cos z +(y+ 1) sin-x at the point (0,0, T/6)

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Q: .3 *csy +a Sina, If f(x,y) = e which of the following is Correct ? A. fa(Z,4) = e*(o54+3x? Sinstaš…

A: differentiate partially with respect to x and y respectively.

Q: b) Find the potential P(x,y) attached to the exact ODE 2x sin(y) + x² cos(y) y' = 0 %3D

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Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

A: Differential equation is, y''+4y'+20y=23sint-15cost Given conditions is, y0=-1y'(0)=1

Q: 1. e+sin z- COs I 2e-u(t)dt

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Q: 4 (y3- y?sinx+3e3*)dx+ (3xy² +2ycosx+)dy=0 Select one: O a. None O b. y°x+y°cosx+e3x +Iny³ = c O c.…

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Q: Q.5) Evalute ar F. ar ds dy R where F(x, y, x) = 2k and r(x, y) = sinx cosy i+ sinx sinyj+ cosx k.

A: To evaluate: The integral ∬R F.∂r∂x×∂r∂yds where F(x, y, z)=2k→ and r(x, y)=sinx cosy i→ + sinx siny…

Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: Find the solution of (x + sin y) dæ + (xcosy – 2y) dy = 0 æcosy y? = C ㅇ 글2 + zcosy - y2 = C '글교2…

A: Solution: Given x+sin ydx + xcos y-2ydy=0

Q: r(t) = (4 sint- 4t cos t,4 cos t+ 4t sin t), for 0sts, 2

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Q: Find r(t) for r'(t) = 2/ti + 3 cos(2nt)j – e-'k and the initial condition r(0) =i+2j

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Q: (xyz)3= ay a (x?z)= 군e le*)= 군e a(xyz)= %3D (x²z) = le*) = %3D (cos xy)= XE (e**) = %3D

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Q: z = 2ev-sinx – 3e*cos(y) find: Ве ww m az ,c). ду a2z (n I a2z а) (q-dexp дхду" дудх URGENTTTT!!!!!!

A: Given function is

Q: 3. dr = b(cos e dr +r sin e d e) (b is a constant). Answer: r = C(1 - b cos e) 4. y Inx In y dx + dy…

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Q: dz dz and du Use an appropriate form of the chain rule to find dv' z = =; x = 14 cos u, y = 5 sin v…

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Q: b. h(2) = (9z +4)i, h®(2) e. y = (t³ – Vī)-3.2, y" %3D c. f(r)= sin(coS r), f"(x) f. y = r+(1– r)²,…

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Q: (ii) (D² + D')u = cos px cos qy u = cos px cos gy (iii) (D²- DD'- 2D)u = (v - 1)e*

A: In the given question we have to find the solution of second and third part of the given question,…

Q: What is the general solution of (x + y) da + tan xdy =0 ? %3D O zsinx + cos a + ysina O zsinx + cos…

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.