# IB math project

Extracts from this document...

Introduction

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My conjecture, for the function bounded by between ‘a’ and ‘b’, is, the ratio of area A to area B is equivalent to the ratio of n to 1. | |||||

## Test- nΖ+
- Fraction
- Negatives
- Irrational Numbers
| 1) nΖ+ | ||||

n=3 | n=5 | ||||

2) Fractions | |||||

3) Negatives | |||||

For all values of n in, no values exist in the region bounded by 0 and 1; therefore no conjecture can be inferred. | |||||

4) Irrational Numbers | |||||

| ## Bounds 0 to 2 | ## Bounds 1 to 2 | ||||

## TEST | ||||||

Bounds 0 to 2 | Bounds 0 to 3 | Bounds 2 to 4 | ||||

My conjecture is valid for all functions of |

Middle

For Negative Bounds:

## Bounds –1 to 0

The conjecture of n:1 is the exact opposite for conjecture of the negatively bounded regions in quadrant III. (1:n)

If a set of positive bounds were to be changed to negative, then the ratio between A and B in the positive bounds would be equivalent to that of B and A in the negative bounds. (see diagram explanation below)

As mentioned in question 2, my conjecture, of n to 1, holds true for all ratios between areas A and B, if a<b; as long the function in question is . Proof: | ||

With the function in question being |

Conclusion

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My conjecture, for the function revolved around the y-axis, bounded by between ‘0’ and ‘1’, is, the ratio of area A to area B is equivalent to the ratio of 1 to 2n. In correlation to the ratio of the function revolved around the x-axis, the ratio between area A and area B is the exact opposite. | |||||

## Test- n=3, n=5
- Fraction
Different Bounds | n=2 | n=5 | |||

2) Fractions | |||||

3) Bounds | |||||

Bounds 0 to 2 | Bounds 1 to 2 | ||||

Proof: With the function in question being rotated around the x-axis, I was able to calculate area A by finding the intregal using the shells method, and by using simple international methods I was able to determine area B. The ratio between area A and area B is 2n to 1 (refer to diagram on the right) |

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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