09-10-2009-lecture

09-10-2009-lecture - A. The picture above shows a portion...

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A. The picture above shows a portion of the unit circle in the x - y -plane, as well as a ray OB that makes a positive angle of θ radians with the positive x -axis. 1) What are the lengths of the following segments: OB , OD , BD , DA , AC ? 2) What are the coordinates of the following points: B , C , D ? 3) What is the area of triangle OAB ? 4) What is the area of sector OAB ? (Hint: This sector makes up a fraction of the circle equal to θ 2 π , while the area of the circle is π .) 5) By comparing the areas of triangle OAB and sector OAB , show that 0 < sin θ < θ when θ is a small positive angle. 6) READ the Squeeze Theorem on page 99. What does 5) imply about lim θ 0 + sin θ ? Is the sine function continuous from the right at 0? 7) Is it continuous at 0? 8) By comparing the length of segment DA with the length of segment DB , show that 1 - θ < cos θ < 1 for small positive θ . 9) What does this imply about lim θ 0 + cos θ ? 10) Is the cosine function continuous at 0?
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This note was uploaded on 11/23/2011 for the course MATH 1551 taught by Professor Malisoff during the Fall '08 term at LSU.

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09-10-2009-lecture - A. The picture above shows a portion...

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