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Assignment 1 Question A

Posted by ra

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Assignment 1 Question A
February 16, 2010 04:47PM

Registered: 15 years ago
Posts: 133
Rating: 0

I've determined that g₁(x) diverges and g₂(x) converges but I have no idea why. None of the options given seem right.

The most relevant text from the textbook on page 55 says:

Quote

It appears that the different behaviors depend on whether the slope of the curve is greater, less, or of opposite sign to the slope of the line (which equals +1).

Has anyone figured out which is which?

And what exactly is meant by 'interval of convergence' in the questions?

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BlaXpydo

Re: Assignment 1 Question A
February 16, 2010 07:19PM

Registered: 14 years ago
Posts: 269
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If I understand correctly, the interval of convergence is when |g'(x)| < 1. Will check it out.

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Re: Assignment 1 Question A
February 17, 2010 03:10PM

Registered: 15 years ago
Posts: 133
Rating: 0

Thanks. You're right.
Becomes clear when you graph |g'(x)|

I did this in octave:

fplot ("[x, 3+x-x^2, 0.000001*x+1, abs(1-2*x)]", [-2,2])