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Need to investgate the ratio of the areas formed when y=x

1. Given the funtion y=x

Find the ratio of area A : area B

now this is where i had trouble

Calculate the ratio of the ares for other functions of the type y=x

2.Does your conjecture hold only for areas between x=0 and x=1? Examine for x=0 and x=2, x=1 and x=2, etc.

3. Is your conjecture true for the general case y=x

Area A: y=x

Area B: y=x

4. Are there general formulae for the ratios of the volumes of revolution generated by the regions A and B when they are each rotated about

a) the x-axis?

b) the y-axis?

State and prove your conjecture

I can do the very first part of this rather easily but I'm having trouble making the conjcture because although it doesn't have to be correct, I do have to prove it later on. Questions 3 and 4 are the ony real problems so ny help with this would be of a major assistance to me. Much Thanks

^{n}is graphed between two arbirary parameters x=a and x=b such that a<b1. Given the funtion y=x

^{2}, consider the region formed by this function from x=0 to x=1 and the x-axis. Label this area B. Label the region form y=0 to y=1 and the y-axis area A.Find the ratio of area A : area B

now this is where i had trouble

Calculate the ratio of the ares for other functions of the type y=x

^{n}, n [tex]\in[/tex] Z+ between x=0 an x=1. (not to complex but) Make a__conjecture__and test your conjecture for other subsets of the real numbers.2.Does your conjecture hold only for areas between x=0 and x=1? Examine for x=0 and x=2, x=1 and x=2, etc.

3. Is your conjecture true for the general case y=x

^{n}from x=a to x=b such that a<b and for the regions defned below? If so prove it; if not explain why not.Area A: y=x

^{n}, y=a^{n}, y=b^{n}and the y-axisArea B: y=x

^{n}, x=a, x=b and the x-axis4. Are there general formulae for the ratios of the volumes of revolution generated by the regions A and B when they are each rotated about

a) the x-axis?

b) the y-axis?

State and prove your conjecture

I can do the very first part of this rather easily but I'm having trouble making the conjcture because although it doesn't have to be correct, I do have to prove it later on. Questions 3 and 4 are the ony real problems so ny help with this would be of a major assistance to me. Much Thanks

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