Unit Circle Approximation and Limits

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What is the main focus of this lesson?

Estimating the limit of a function

Defining the limit of a function

Illustrating the limit of a function using tables of values (correct)

Calculating the area of a circle

Which competency does this lesson aim to address?

STEM_BC10LC-IIb-2

STEM_BC11LC-IIIa-1 (correct)

STEM_BC12LC-IVc-4

STEM_BC9LC-Ia-3

What is the purpose of Part A of the worksheet?

Practice estimating limits

Learning one-sided limits

Review on the area of a circle (correct)

Introduction to limit functions

How does changing the values of 𝑛 affect the area of the polygon?

Increases Signup and view all the answers

At what value should the radius 𝑟 be set according to the procedure?

$1$ Signup and view all the answers

What is the focus when exploring the GeoGebra applet?

Estimating the limit of a function Signup and view all the answers

What is the formula for the area of a circle?

$ ext{Area} = ext{radius}^2 imes ext{pi}$ Signup and view all the answers

If a circle has a radius of 3, what is the area of this circle?

9 pi Signup and view all the answers

What is the area of a triangle with base 5 and height 8?

20 Signup and view all the answers

In the given data table, what is the area of a decagon?

$10 \times \text{Area of Triangle}$ Signup and view all the answers

If you double the radius of a circle, what happens to its area?

Area quadruples Signup and view all the answers

What happens to the area of a circle as the number of sides in the inscribed polygons increases?

The area approaches the actual area of the circle Signup and view all the answers

What term is used to describe the value that a sequence of values approaches?

Limit Signup and view all the answers

What is the relationship between the area of the inscribed polygon and the area of the unit circle?

The area of the inscribed polygon is always less than the area of the unit circle. Signup and view all the answers

What concept is illustrated by dividing a square into smaller parts to approach certain values?

Limit approach Signup and view all the answers

What happens to the areas of the polygons as the number of sides of an inscribed polygon increases indefinitely?

The areas become closer to the area of the unit circle Signup and view all the answers

Why is the area of the inscribed polygon limited to not exceed 𝜋?

Because the polygons are inscribed in the unit circle Signup and view all the answers

What is being approached by a sequence of values when determining the area of a unit circle?

The limit of the areas of polygons as sides increase indefinitely Signup and view all the answers