Given the boundary of the surface of a cylinder 0 < p < 3,

Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

A: Given right angle triangle has vertices  (0, 0), (0, b), and (a, 0), where a &gt; 0 and b &gt; 0.…

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: ind the maximum and minimum values of the function f(x, y, z) = ax + by + cz, where a, b, c are…

A: In the given question, maximum and minimum values of the function f(x, y, z) = ax + by + cz, where…

Q: Find Əz ?х Əz da Əz ду = ab brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)). • Put…

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Q: Verify Stokes theorem ㅋ F² = (2x²-y)=² - y²²} - y²zk, where -y s is of and the the с upper sphere.…

A: Given: F=2x-yi-yz2j-y2zk where S is the upper half surface of sphere x2+y2+z2=1 and C is its…

Q: Evaluate the line integral, where Cis the given space curve. xevz ds, C is the line segment from (0,…

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Q: Advanced Math 4. Let f: S^2 → S^2 be a reflection of the sphere which leaves the plane H = {(x, y,…

A: Given Plane : H =x,y,z100x +239x+11z=0 To find: All great circles which are invariant under f.

Q: Let T be the tetrahedron with vertices at the origin and (4,0,0), (0,5,0) and (0,0,2). A fluid flows…

A: Given, Vertices of the Tetrahedron are, , , and Velocity of fluid:

Q: Given the Surface z = 8 - 4x² - 2y2, find the direction of the maximum slope at point P (1,1,2) and…

A: here we can use the properties of gradient of  a curve to find the direction of maximum change.

Q: ketch the surface 13zS 19-x² - y' and x'+y' <1

A: To sketch the graph:

Q: Find the area of the surface generated when the given curve is revolved about the y-axis. y-(3x)13,…

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Q: Prove that at the point of intersection of the surfaces x² + y² = 2², z = a tan` X where y = x tan…

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Q: where y . Prove that at the point of intersection of the surfaces (4) y __x² + y² = z², z = a tan` =…

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Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: 1. Find the minimum and maximum distance between the sphere x^2+y^2+z^2= 7/2. And the point (1,2,3).…

A: You have posted multiple questions, we will give an answer to the first question, if you need help…

Q: A thin metal plate of uniform density covers the area between the curves y = 2+ 6x – x² and y = 2 –…

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Q: The level surface of f(x, y, z)=Vx²+y² -5_of height 2 is O a. A circle of radius /2 O b. A cylinder…

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Q: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

A: The given surface is  f(x,y)=z=(x2+y2)2  ...........(1); we have to find the tangent plane at point…

Q: Choose the equation that represents the * graph of the cylindrical surface below -25 -20 -15 -15 -10…

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Q: Find the area of the surface generated by revolving the curve about the indicated axis. 36) y=V4x -…

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

Q: 3. Find the length of the curve y = x – In x, 1<x < 4. 1. Find the area of the surface obtained by…

A: The solution is given as follows

Q: If z = f (x, y) is a smooth continuous surface such that f.(a,b) =0 and f,(a,b) =0 then what can you…

A: Please see the explanation below

Q: erustion for the tangena plare to the Surface = 12 at the point L-2,1,3) Find an Siven by x2y2z

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Q: Determine if F(n.y,z) =x+y+Z have a maximum/minimum value when m,9, z) lies on unit sphere:x'+yiZ=1•…

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Q: u?i + uvj + v²k bounded by the Find the area of the surface R(u, v) inequalities |u| < 2, \v| < 2.

A: Given that, R(u,v) = u2 i + uv j + v2 k With  We have to use the formula of surface area, Here, Ru…

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: Find the surface in the accompanying area of the heli r(r,0) = (rcos0)i+(r sin 0) j + Ok, 0s0<2r,…

A: Introduction: The formula for the surface area of the function r(r,θ) is given by,…

Q: The intersection between the surface x + y + z = 4 and the circle x2 + y? = 16,z = 0 is Your answer:…

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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.