Simple and short true-false tasks regarding Precalculus

Question

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

Answer 1

1. Right
2. Wrong (What is the boundary of $\{0\}$ in $\mathbb R$? What is its set of cluster points?)
3. Right
4. Right
5. Right
6. Right
7. Right
8. Right
9. Wrong (it isn't defined there)
10. Right
11. Wrong (think about what this function is)