I attached a picture of the question and the reference figure. thank you! An arc $ PQ $ of a circle subtends a central angle $ \theta $ as in the figure. Let $ A(\theta) $ be the area between the chord $ PQ $ and the arc $ PQ $. Let $ B(\theta) $ be the area between the tangent lines $ PR, QR $, and the arc. Find\[\lim_{{\theta \to 0^+}} \frac{{A(\theta)}}{{B(\theta)}}\] The image presents a geometric diagram involving a circle and two overlapping sectors centered at point Q. Here is a detailed description:- **Circle**: The left-hand side of the image contains a circle with the center marked at point Q.- **Sector**: There is a circular sector denoted by $ A(\theta) $ in red, which is part of the circle with a central angle of $ \theta $.- **Triangle**: To the right, there is a triangle $ \Delta PQR $ with its vertex at R, sharing the segment $ \overline{PQ} $.- **Blue Region**: Another region $ B(\theta) $ is outside the circle but part of the triangle $ \Delta PQR $. It shares the same central angle $ \theta $ as the red sector.- **Points**: Important points in the diagram are labeled as Q (center of the circle and vertex of both sectors), P (intersection of the circle and the boundary of sectors), and R (another vertex of the triangle).The diagram illustrates geometric concepts involving angles, sectors of a circle, and overlapping segments, demonstrating how sectors and triangles can share common central angles.

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Description: I attached a picture of the question and the reference figure. thank you! An arc $ PQ $ of a circle subtends a central angle $ \theta $ as in the figure. Let $ A(\theta) $ be the area between the chord $ PQ $ and the arc $ PQ $. Let \( B(\t

Since PR is tangent so PR is perpendicular to OP where O is the center. Thus, PR=r×tanθ2.…

Math

Advanced Math

An arc PQ of a circle subtends a central angle 0 as in the figure. Let A(0) be the area between the chord PQ and the arc PQ. Let B(0) be the area between the tangent lines PR, QR, and the arc. Find A(0) lim 00+ B(0)

An arc PQ of a circle subtends a central angle 0 as in the figure. Let A(0) be the area between the chord PQ and the arc PQ. Let B(0) be the area between the tangent lines PR, QR, and the arc. Find A(0) lim 00+ B(0)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I attached a picture of the question and the reference figure. thank you!

An arc $ PQ $ of a circle subtends a central angle $ \theta $ as in the figure. Let $ A(\theta) $ be the area between the chord $ PQ $ and the arc $ PQ $. Let $ B(\theta) $ be the area between the tangent lines $ PR, QR $, and the arc. Find

\[
\lim_{{\theta \to 0^+}} \frac{{A(\theta)}}{{B(\theta)}}
\]

The image presents a geometric diagram involving a circle and two overlapping sectors centered at point Q. Here is a detailed description:

- **Circle**: The left-hand side of the image contains a circle with the center marked at point Q.
- **Sector**: There is a circular sector denoted by $ A(\theta) $ in red, which is part of the circle with a central angle of $ \theta $.
- **Triangle**: To the right, there is a triangle $ \Delta PQR $ with its vertex at R, sharing the segment $ \overline{PQ} $.
- **Blue Region**: Another region $ B(\theta) $ is outside the circle but part of the triangle $ \Delta PQR $. It shares the same central angle $ \theta $ as the red sector.
- **Points**: Important points in the diagram are labeled as Q (center of the circle and vertex of both sectors), P (intersection of the circle and the boundary of sectors), and R (another vertex of the triangle).

The diagram illustrates geometric concepts involving angles, sectors of a circle, and overlapping segments, demonstrating how sectors and triangles can share common central angles.

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