(iii) 3rd subplot is A butterfly curve using polar coordinates: 2a - I r = esina – cos(4a) - sin( 24 -), where a takes 500 values from O to 8 T.

Q: The transform curve of polar equation r 4 cos@+4 sin e to rectangular coordinates (x-2)° – y² = 8…

A: Given that: r=4cosθ+4sinθ

Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

A:

Q: Consider curve C of equation (x2 −2y + y2)2 = x2 + y2. Among the options indicated,select the one…

A: Consider curve C of equation (x2 −2y + y2)2 = x2 + y2. Among the options indicated,select the one…

Q: Consider curve given in polar coordinates by Find the derivative r = 8 cos 0,0 ≤ 0 ≤T/2, dr do -8…

A: The given curve is: r=8cosθ;  0≤θ≤π2. To Do: Find the derivative drdθ. Compute the surfaced area…

Q: Graph the following polar function r = f(0) =V4-3 sin 20 on the interval 0<0<2n , and find %3D the…

A: We have polar function given and we have to graph the function and find the area of this sector.

Q: Consider the polar curves C₁ : r = 2 - cas 0 and C₂: r = 2 + 2 cos 0, 0 € [0, 2πC). (1.) Show that…

A:

Q: 6) Graph in polar coordinates r = 1+ cos 8.

A: We have to plot the graph of the given function in polar co-ordinate.

Q: The polar equation r = a+a cos 8, where a > 0, has a tangent line at (0, 7)

A:

Q: Find the length of the curve given in polar form as r= e,- <o<a a)2/2 sinh(7) b)sinh(") c)2 sinh(7)…

A:

Q: 13) Find as all polar points (r, 0) of horizontal and vertical tangency to the curve: x = cos(20) y…

A:

Q: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: 3. Consider the curve C of equation 4ry r² + y²" Among the options indicated, select the one that…

A:

Q: First part of the question is that convert the following Cartesian coordinates to the corresponding…

A:

Q: Sketch the curve with polar equation r = cos(30), 0 ≤ 0 < 2π, plotting only the points with r≥ 0 and…

A:

Q: Q2 Find the points of intersection of the polar curves r=1+cos 9 and r= -cos

A: Point of intersection of the Polar curve

Q: Find a Cartesian equation for the curve represented by the given Polar equation. (a) r = -2 (b) T =…

A: We have polar form equationWe have to convert it in cartesian form

Q: 12. (a) Sketch the curve in the polar coordinate system with directions, (b) Find the values o for…

A:

Q: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: 5. (i) Find the polar coordinate of the point P(x, y) = (1, v3).Plot the graph (ii) Find the…

A:

Q: Plot the following curves in polar coordinates. 50 (52) 1. r = 2 + cos

A: We have to graph the given polar curve.   According to our guidelines we can solve only one question…

Q: 6 (1). Consider the curve C of equation (x²-2y+y²)² = x²+y². Among the options listed, select the…

A: We know that a polar coordinate is represented by r, θ, where r is the length with r=x2+y2 and θ is…

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.