How do you find the maximum R value of a polar equation?

The maximum value of r=2+2cosθ occurs when cosθ is a maximum, which is when cosθ=1 or when θ=0. Substitute θ=0 into the equation, and solve for r. The point (4,0) is the maximum value on the graph.

How do you find the length of a curve in polar form?

To find the area between two curves in the polar coordinate system, first find the points of intersection, then subtract the corresponding areas. The arc length of a polar curve defined by the equation r=f(θ) with α≤θ≤β is given by the integral L=∫βα√[f(θ)]2+[f′(θ)]2dθ=∫βα√r2+(drdθ)2dθ.

How do you find the limit of integration in polar coordinates?

To determine the limits of integration, first find the points of intersection by setting the two functions equal to each other and solving for θ: 6sinθ=2+2sinθ4sinθ=2sinθ=12. =4π. Find the area inside the circle r=4cosθ and outside the circle r=2.

What is the minimum distance from the origin to the curve?

The shortest distance will be along a normal to the curve. Differentiating y = 1/x gives dy/dx = -1/x². This means that the gradient of the normal at (x,y) will be x². A graph of y=1/x indicates that the shortest distance will be for x slightly below zero.

What is the maximum R value?

approximately R-45
Example values Vacuum insulated panels have the highest R-value, approximately R-45 (in U.S. units) per inch; aerogel has the next highest R-value (about R-10 to R-30 per inch), followed by polyurethane (PUR) and phenolic foam insulations with R-7 per inch.

What is the length of the arc of a circle?

The arc length of a circle can be calculated with the radius and central angle using the arc length formula, Length of an Arc = θ × r, where θ is in radian. Length of an Arc = θ × (π/180) × r, where θ is in degree.

Is arc length the same as length of curve?

Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment is also called rectification of a curve.