Let be an integer such that exists, where is greatest integer . Then is equal to

Question

Let  be an integer such that  exists, where  is greatest integer . Then  is equal to

Canvas Classes · Accepted Answer

🧠 Reading the Question — Floors Jump When the Inside Hits an Integer

This limit has two floor functions, top and bottom. Whenever you see  in a limit, the very first thing to check: does the inside expression hit an integer at the limit point?

Look at  as . We get , which is an integer. That means  jumps right at . So the numerator has different values from the left and from the right. For the overall limit to exist, the denominator must also jump at  in a way that makes both ratios equal. Th

More questions from this chapter

More questions from this chapter