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# IB math project

Extracts from this document...

Introduction

 1

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

1. nΖ+
2. Fraction
3. Negatives
4. 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

 2

## TEST

Bounds 0 to 2

Bounds 0 to 3

Bounds 2 to 4

My conjecture is valid for all functions of

Middle

and , then my conjecture, of n to 1, holds true for all ratios between areas A and B.

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)

 3

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

 4b.

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

1. n=3, n=5
2. 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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