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[Community Question] Calculus: Simple and short true-false tasks regarding Precalculus

One of our user asked:

Here are few of the questions from the previous years' exams. I've chosen the ones I'm not sure about. It's a simple TRUE/FALSE task. Would anyone be able to verify my solution? Some of my answers are good, some are just random guess according to my intuition. I don't really need a detailed explanation... Thanks!

  1. Domain of $f'$ is contained within domain of $f$. - TRUE
  2. Boundary point of set A is also a cluster point of that set. - TRUE
  3. Every increasing sequence and bounded above is convergent. - TRUE
  4. Every increasing sequence and bounded below is convergent. - FALSE
  5. Every increasing sequence is always bounded below. - TRUE
  6. Every sequence is discontinuous function. - FALSE
  7. Every sequence is continuous function. - TRUE
  8. Every function integrable on $<a, b>$ is continuous on $<a, b>$. - FALSE
  9. Function $f(x) = \ln{|x|}$ is discontinuous at $0$. - TRUE
  10. The continuity is necessary for differentiability. - TRUE
  11. Function $f(x) = \frac{x}{|x|}$ is monotonic. - FALSE

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