Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

Q: Indicate whether the following statement is true or false. siont e dy dx = fSi P(cos(0)? dr d0 False…

A: Double Integrals conversation to polar coordinates

Q: 3) eYsinx dx = cos?x dy 4) y' + (÷) y = xy?

A: First question we can easily solve using veriable separable method. Second question we can use from…

Q: 4X dy 2siny ?) S dy sinzx e 3) S sin? dx

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Q: F ind So S. eu dy dx.

A: Use the concept of reversing the order of integration. While integrating with respect to one…

Q: Given z = 9t – 11 and y = 81 sin t dy (ii) 9*sin(t)/0 dx²

A: Here we have to differentiate the given function

Q: /2 y sin a dy de 4. evaluate

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Q: Exercise: Answer the following by finding dy/dx. 5sin-1 # – cosh x (a) y = Vsec4 x + In 7 4 (b) + In…

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Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

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Q: (a) If y = tan x, prove that y = 2(y2 + 1)(3y2 + 1). (b) Find y' for y cos(sin?x). %3D %3D dy (c) If…

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Q: d Q 3. Prove that tanx dx sec?x. =

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Q: Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 d0) %3D

A: Separation of variables.

Q: dy given that: dx (a) Find 3yx + sin(2y – 4) = /(2y)

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Q: dy If x = sin? (u) and y = cos2(u), then %3D dx

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Q: Let w = 4e" dx /A dy + aeª dx ^ dz and n = 7e*Y dx + 8e² dy + eY dz, where a E R. Find the value of…

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Q: dz Find dy x? sin(2y – 5z) =1+y cos(6za)

A: The given equation is: x2sin(2y-5z)=1+ycos(6zx) To find ∂z∂y, differentiate above equation w.r.t. y…

Q: dy If x = a (0 – sin 0), y= a (1– cos 0), then find dx |

A: Introduction :

Q: dy Find for y = sin (2x +3) da %3D Ans=

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Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

A: We will prove the given statement.

Q: Given z 13t 9 and y- 169 sin : dy dx d²y da?

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Q: dy Let y=e* sin 3x. Show that 3e-2* cos 3x - 2y. dx -2x d'y = -13y-4- dr Hence show that dx

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Q: Let w = (sin(x) +7 cos(y)) dy ^ dz + (2³ – y cos(x)) dz A dæ + 14xyz da A dy. Find dw. dw = dx A dy…

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Q: Given z = 8t – 18 and y= 64 sin t dy (i) da dy (ii) dx?

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Q: Given x 13 In(t) and y = 169 t2 then find %3D dy dx dy dæ?

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Q: If x = t +cos t, y= sin t, find d^2/dx^2

A: Given that      x=t+cost , y=sint  Here we have to find d2y/dx2 .

Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Te 2=tnx then prove thot dx 28 Snメー tty? 1+xて

A: We have to use proper calculus applications.

Q: z sin a dy dæ dz

A: The question is taken from the calculus inwhich we have to find the triple integration of the given…

Q: Solve for if y- Ina 2- y?. da MCQ3.pdf dy 2y +1 dx dy 2y +1 dx dy dæ -(2y+1)x 1 dy (2y+ 1)a TERIRS…

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Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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Q: 6 3 oy sin (a? + 3²) dædy Find

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Q: "/2 dx dy = * 4 3 cos X I then k is equal to 6. %3D %3D k

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: 5. Evaluate r'sin(y³) dy dx

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Q: - 403 y = cos dy %3D de

A: Given : y = cose-4θ3

Q: If y = (sin¬1 x)², show that dy (1 – x²) da? dy = 2. dr

A: y=(sin-1x)2 we have to show  (1-x2)d2ydx2-xdydx=2

Q: (a) Find dr dy given that x²y + sin xy = 0.

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

Q: et cos(e') dt = (b) +C 3+4 sin(et) 3/4 sin-1 (c) (승교) dx = 16x?

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Q: The general solution of the DE dx dy = cos?y is

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Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: Given tanh(x)+ tanh (y) = 1, show that, dy 1- y? dx 1- x2

A: We can find the required answer as below

Q: x²+y²` du du =+y dx If u=sin| ,x+y #0,Prove that x =tan u x+y dy

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Q: If x=sin8,y=0 ,y=cosp0,Prove that (1-x') y,-xy,+p°y=0 where y2 d'y dy and y,- dx? dx

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Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: Given x = 13t – 6 and y = 169 sin t dy dx d²y dx? ||

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Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: Given x = 12t – 48 and y= 144 sin t %3D dy dx dy dx?

A: We know dydx=dydtdxdt d2ydx2=ddxdydx=ddtdydxdxdt

Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.