# Thread: Bernouilli & De L´Hospital

1. ## Bernouilli & De L´Hospital

Hello! Can someone explain me how to solve the following expression with the Rule of B&H ?

$\lim (\frac {cos \pi} {n})^n$

im pretty clueless here, so some details would be awesome

2. Originally Posted by coobe
Hello! Can someone explain me how to solve the following expression with the Rule of B&H ?

$\lim (\frac {cos \pi} {n})^n$

im pretty clueless here, so some details would be awesome

What value is $n$ tending to?

3. What is the relationship between Bernouilli and limit problem ? I know we may make use of L'Hospital rule to solve it so you talk about him but i am wondering why you talk about Bernouilli .

4. its intended to go to infinity, sorry i dont know how to do that in latex

5. Originally Posted by coobe
its intended to go to infinity, sorry i dont know how to do that in latex

$\lim_{n\to\infty} (\frac{ \cos{\pi}}{n})^n$
Is it what you are asking ?

6. yes, but N goes to infinity

7. What is the relationship between Bernouilli and limit problem ? I know we may make use of L'Hospital rule to solve it so you talk about him but i am wondering why you talk about Bernouilli .
It is widely understood that Johann Bernoulli developed the mathematics behind what is commonly known as L'Hospital's Rule. It basically came down to the fact that Bernoulli was tutoring L'Hospital, and L'Hospital in turn was recording all of his lectures for use in a book on calculus. The book was published and the rule named after L'Hospital. As credence has been lent to this notion over the years some have started calling it Bernoulli's Rule. It's an interesting idea, and I thought I'd mention it.

8. im a student at a german university of applied sciences and we call it Rule of Bernouilli and De L´Hospital. Never heard of it as only Hospital Rule, except in some english lecture

9. Try limit by taking cos $pi$ as -1 and add and subract -1 and 1 inside the bracket and use $(1+x)^n$ $(1+(x/n))^n = e$ as n tends to infinity.

10. What if you take the absolute value, so the expression ends up:

$
\frac{1}{n^n}
$

And then you use the comparison rule, and compare it with $\frac{1}{n}$?