Thread: Limits of three functions

Could you help me calculate the following limits:









As to the last one I thought I could use but it wouldn't work

Is the first limit equal to 1, the second to 1,5 and the third one to ?

I just did the second one I think it's 3/2. I may have made some computational errors but you simply use l'Hopital's rule twice because you have the form 0/0 twice

Originally Posted by wilhelm

Is the first limit equal to 1, the second to 1,5 and the third one to ?

What an absolutely useless reply!
Can you explain any of that? I doubt it.

@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.

Originally Posted by wilhelm

@Plato But of course I can. To compute the first limit I simply used the squeeze theorem and floor function inequality.

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.