Let denote the greatest integer and . Then the function, is discontinuous, when is equal to:

Question

Let  denote the greatest integer  and . Then the function,  is discontinuous, when  is equal to:

Canvas Classes · Accepted Answer

🧠 Compute  First, Then Check Each Option for Discontinuity

The first job: find .

For small :  is large positive. , so . Since ,  as . So the limit is 4.

So . Check each option's value:

- .
- .
- .
- .

Now . It's discontinuous where  jumps AND .

jumps when  is integer, i.e.,  for non-negative integer .

when  is integer.

So discontinuity happens at  where  is NOT a perfect square (so  is irrational, and ). For perfect-square ,  is integer and , killing the jump.

🗺️ Working It Out

Fin

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