Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I can solve the question limit of function like $$ \lim\limits_{x\to\infty}\frac{\lfloor x-3\rfloor}{x-1} $$ but I cant solve the question like $$ \lim\limits_{x\to n^\pm}\frac{\lfloor x-1\rfloor}{x-1}\\ \lim\limits_{x\to n^\pm}\frac{\lfloor x\rfloor}{x-1} $$ Please help me.

share|improve this question
    
What have you tried? It isn't clear what you mean in the first line. –  user17794 Jul 27 '12 at 5:22

1 Answer 1

I am assuming that these are the questions your are asking and that $n$ is an integer.

As $x$ approaches $n$ from below, $\lfloor x-1\rfloor=n-2$; therefore, $$ \lim_{\large x\to n^-}\frac{\lfloor x-1\rfloor}{x-1}=\frac{n-2}{n-1} $$ As $x$ approaches $n$ from above, $\lfloor x-1\rfloor=n-1$; therefore, $$ \lim_{\large x\to n^+}\frac{\lfloor x-1\rfloor}{x-1}=\frac{n-1}{n-1} $$ With these as examples, try the others.

share|improve this answer

Your Answer

 
discard

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.