Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have to find the vertical asymptote of $y=2x-\arccos(\frac{1}{x})$. So I have to find the limit of the function when $x$ approaches zero. In my textbook it says that the vertical asymptote does not exist for this function ..why? For $x\to0$ the function goes to infinity so $x=0$ should be a vertical asymptote?

share|cite|improve this question

The cosine of any angle is between $-1$ and $1$, so if $|x|<1$, $\arccos\frac1x$ is undefined. Thus, the function $$f(x)=2x-\arccos\frac1x$$ is undefined in the neighborhood $(-1,1)$ of $0$ and cannot have a limit as $x\to 0$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.