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AP Calculus AB Free Response Question Presentation

AP Calculus AB Free Response Question Presentation. By Kevin Kong Period 2 . 2002 AP Calculus AB Free Response Question. 2002 AP Calculus AB Free Response Question. Starting with Part A: Finding the Area of the region.

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AP Calculus AB Free Response Question Presentation

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  1. AP Calculus AB Free Response Question Presentation By Kevin Kong Period 2

  2. 2002 AP Calculus AB Free Response Question

  3. 2002 AP Calculus AB Free Response Question

  4. Starting with Part A: Finding the Area of the region In order to find the Area of the Region enclosed by the graphs of F and G between x = ½ and x=1one must use the integral equation… …and substitute all the known variables, where a and b corresponds to the interval.

  5. Starting with Part A: Finding the Area of the region After substitution, the derived equation should look a little something like this: After plugging that equation into the calculator, one should arrive at the answer of 1.222 or 1.223.

  6. 2002 AP Calculus AB Free Response Question

  7. Continuing to Part B: Finding the Volume of the region In order to find the Volume of the Region enclosed by the graphs of F and G between x = ½ and x=1 and revolved around the line y=4, one must use the integral equation…

  8. Continuing to Part B: Finding the Volume of the region To determine which function comes first, the perspective of the line, in which the function is revolved, must be considered. The function further away from the line comes first.

  9. Continuing to Part B: Finding the Volume of the region • After substitution, the derived equation should look a little something like this: After plugging that equation into the calculator, one should arrive at the answer of 23.609

  10. 2002 AP Calculus AB Free Response Question

  11. Continuing to Part C: Finding the Absolute Minimum and Maximum values of the region • To attempt a problem like this, we must first realize that in order to find the absolute values, we must identify where the function equals zero. To do so, one must find the derivative of the function.

  12. Continuing to Part C: Finding the Absolute Minimum and Maximum values of the region • Absolute minimum value and absolute maximum value occur at the critical point or at the endpoints.

  13. Continuing to Part C: Finding the Absolute Minimum and Maximum values of the region • Considering the closed interval, we must determine which of these points are the absolute values. The Absolute Minimum is 2.330 The Absolute Maximum is 2.718

  14. Citations • http://www.flashcardmachine.com/exponential-and-logarithmicfunctions.html (Graph of Functions) • http://www.collegeboard.com/prod_downloads/ap/students/calculus/calculus_ab_frq_02.pdf (Question) • http://fc.bullis.org/~stacey_Roshan/FOV2-0001E0A5/FOV2-00026983/S015FAFF4.76/2002%20Scoring%20Guidelines.pdf (Answer Key)

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