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

Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

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Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: Ex 21Eulers method dy-y= - y Xーツ ーメー

A: We have to use the Euler's Method to solve                           dydx=y'=x-yx+y, y0=1,…

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Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

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Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

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Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

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Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

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A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: 1. Obtain the par hicul ar foluhon 4 DE . 9xy dy a. oy dx = ; uh en x= 2,y=1 b. 4xy dy = 2y (I+ y?)…

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Q: Using the approximation dy dy * Yn+1 - Y, and that dr 1, y = 2 dr h when r= 0. Then, y, = A h-2 h+2…

A: Use the approximation hdydxn≈yn+1-yn and that dydx=1, y=2 when x=0. Then y1=?

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

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Q: : 0s 0s n, Os zs 1, 6Vzs rs 6}. Let E= Compute y?e(x2+y?)³ dv•

A: Given that, Let E=r,θ,z : 0≤θ≤π, 0≤z≤1, 6z≤r≤6 compute ∬∫Ey2ex2+y22dV

Q: 3. If x = (sin t+cos t), y = (cos t-sin t), (1 < t < 4), evaluate ip, dt. dt dt

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Q: dy sin(x + y) dx

A: Given , dydx=sin(x+y) Substituting u=x + y dudx=1+dydx Substituting dydx=sin(x+y) in dudx=1+dydx…

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A: We can use the concept of Laplace transform in order to solve the given problem.

Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

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Q: 12. Express ſ S S Vxyz(1 – x – y– z) dx dy dz in terms of u, v,w given that x + y +z = u, y+z = uv…

A: Express the Mathematical expression for Jacobian transformation of x=x(u,v,w),y=y(u,v,w) and…

Q: 1 If z = 5xe2xy and x =/t,y=. Then, dz at t = 5 is equal to dt the value of 2/5 V5 Select one: True…

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Q: s zy dydz こミ0

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

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

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Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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