Could you help me calculate the following limits:
As to the last one I thought I could use but it wouldn't work
@Plato But of course I can. To compute the first limit I simply used the squeeze theorem and floor function inequality. As to the second one I could use the de l'Hospital theorem but I used simple trigonometric transformations instead. And when it comes to the third one I just noticed that the limit is equal to derivative of .
I posted the answers simply because I didn't feel like writing the whole solutions. I'm sorry.
It would have helped if you had said this problem involved the "floor function"! What you wrote, , is NOT the "floor function", it is just a complicated way of writing .
If you wanted the floor function, write it as .
As to the second one I could use the de l'Hospital theorem but I used simple trigonometric transformations instead. And when it comes to the third one I just noticed that the limit is equal to derivative of .
I posted the answers simply because I didn't feel like writing the whole solutions. I'm sorry.