MHB Continuous, discontinuous and piece-wise function

Tracy18
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help me please to determine what are the equations i need tofinish my activity. Thankyou
 
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Have you tried anything?
 
Nope I don't know where to stat
 
Tracy18 said:
Nope I don't know where to stat
What are the three types of discontinuites?

-Dan
 
It is very strange that this says "should have two continuous point(s)". This function will necessarily have infinitely many points of continuity! I presume it means that two of the five break points are to be points of continuity.
 
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I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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