Have a couple of questions that I've been stuck with for some time. Would greatly appreciate the help. No idea how I should approach these questions and how do I start.(adsbygoogle = window.adsbygoogle || []).push({});

6. Suppose that a function f is continuous on the closed interval [0,1]and that 0≤f(x)≤1 for every x in [0,1].Show that there must exist a number c in [0,1] such that f(c)=c(c is called a fixed point of f).

(7) Is it true that if you stretch a rubber band by moving one end to the right and the other end to the left, some point of the band will end up in its original position? Give reasons for your answer.

(8) Is there any reason to believe that there is always a pair of antipodal (diametrically opposite) points on Earth’s equator where the temperatures are the same? Explain.

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# Homework Help: Questions Regarding Limits

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