Could you help me calculate the following limits:

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

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- December 18th 2012, 12:22 PMwilhelmLimits 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 - December 18th 2012, 12:58 PMwilhelmRe: Limits of three functions
Is the first limit equal to 1, the second to 1,5 and the third one to ?

- December 23rd 2012, 05:05 PMqnohraRe: Limits of three functions
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

- December 23rd 2012, 05:58 PMPlatoRe: Limits of three functions
- December 23rd 2012, 09:55 PMibduttRe: Limits of three functions
- January 3rd 2013, 06:18 AMwilhelmRe: Limits of three functions
@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. - January 3rd 2013, 06:31 AMHallsofIvyRe: Limits of three functions
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 .

Quote:

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.