Find the arc length of y =x2/3 , -1

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Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: i) Pre that at the Point x- of the Crerve Y: 4m-S, the radices of cervatune f' 5is

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Q: c) lime**sin.x =

A: Limx-infinity sinx

Q: Find if y = tan- 5). Select one: A. 1-) В. 1+ (1 – 2)* C.d - 2 O D. I+ (1 - 1)* OE.+ (1-)

A: Given function is We know that derivative of tan inverse x is 1/1+x^2,so

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Q: x² +y² = 25from x = 2 to x = 4. Find the length of the arc of the circle

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Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

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Q: te: sec(5 x + 4) tan(5 x + 4) dæ

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Q: Find a value for x so that distance from (x,3,6) to the origin is 9

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Q: nd the ndcaed liml lim 15X +3

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Q: xz •Evaluate So So So ²³x² sinydydzdx X

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Q: caluate integra X- Sin

A: Given : The integral is ∫ x sin ( 2x2 )dx .

Q: If secA=x+1/4x ,prove that secA+tanA=2x or 1/2x

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Q: Fins the exact value of each expert if 270*<θ<360*

A: Solve the following

Q: Find the period of the LCG defined by a = 4,b = 0, m = 9. Does the period depend on the seed?

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Q: Q2) a) Find f xein(x²+5) cos(x? + 5) dx

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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.