Unit Circle Approximation and Limits

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Questions and Answers

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?

<p>Increases (B)</p> Signup and view all the answers

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

<p>$1$ (A)</p> Signup and view all the answers

What is the focus when exploring the GeoGebra applet?

<p>Estimating the limit of a function (C)</p> Signup and view all the answers

What is the formula for the area of a circle?

<p>$ ext{Area} = ext{radius}^2 imes ext{pi}$ (D)</p> Signup and view all the answers

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

<p>9 pi (C)</p> Signup and view all the answers

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

<p>20 (D)</p> Signup and view all the answers

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

<p>$10 \times \text{Area of Triangle}$ (D)</p> Signup and view all the answers

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

<p>Area quadruples (B)</p> Signup and view all the answers

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

<p>The area approaches the actual area of the circle (D)</p> Signup and view all the answers

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

<p>Limit (B)</p> Signup and view all the answers

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

<p>The area of the inscribed polygon is always less than the area of the unit circle. (B)</p> Signup and view all the answers

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

<p>Limit approach (D)</p> 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?

<p>The areas become closer to the area of the unit circle (C)</p> Signup and view all the answers

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

<p>Because the polygons are inscribed in the unit circle (D)</p> Signup and view all the answers

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

<p>The limit of the areas of polygons as sides increase indefinitely (B)</p> Signup and view all the answers

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