Consider the graph given in polar coordinates by r=2cos(4@) a)sketch the graph of r(@) when @ is greater than or equal to 0 and less than or equal to pi/4.   b) What is the area enclosed by the graph when @ is greater than or equal to 0 and less than or equal to pi/4?   c)How do you use this to calculate the area enclosed by the graph when @ is geater than or equal to 0 and less than or equal to 2pi.?

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Q: Sketch the regions defined by the polar coordinate inequalities 0 ≤ r ≤ 6 cos θ

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Q: 7. Find all points of intersection of the r= 3sine polar curves: such that r= 1+sine

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Q: Sketch me polar urve =cos(60) %3D and wmpute the tangent linm ar thm Value = 24 TT

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Q: Find the area of the region inside one leaf of the polar graph: r = sin7x

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Q: Find the length of the curve over the given interval.                                     Polar…

A: Given: rθ=5cosθ; θ∈π2,π we know that arc lengthL for any given functionfx over interval a,b is given…

Q: area of one loop

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Q: It can be shown that the polar curve r = a sin(0) +b cos(0), where ab + 0, is a circle. Find the…

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Q: 6. a) On polar graph paper, sketch the cuve given by r = 2 sin(0). b) Find 2 and explain how you…

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Q: Illustrate what are the intersections of polar curves?

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Q: Find the slope of the tangent line to the polar curve r = cos(e) at e =. Enter as an integer or…

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Q: Calculate the area of the region inside the cardioidr = above the polar ray. Show by drawing. a(1 +…

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Q: Find the exact length of the polar curve r cos (0/4). Length = CS Scanned with CamScanner- %3D

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Q: Convert to a polar coordinates. 11. (-4,4) lar form. Show work on separate paper.

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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.