- #1
cateater2000
- 35
- 0
Hi I'm having trouble computing this limit
lim n-> infinity tan(pi/n)/(n*sin^2(2/n))
Any hints would be great
lim n-> infinity tan(pi/n)/(n*sin^2(2/n))
Any hints would be great
cateater2000 said:"How about using the small angle approximations to the sine and tangent"
not sure about that.
And wouldn't l'hopitals be a little nasty? I don't think it'll work out
(tan(pi/n)/n)/sin^2(2/n)
this has form 0/0 so I apply l'hopitals and get something real nasty that won't simplify. I'll try simplifying it sometime tonight though thanks for your help
A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It is used to determine the value of a function at a particular point, and is denoted by the symbol "lim".
Computing a limit can be difficult because it requires a deep understanding of the function and its behavior, especially as the input approaches the desired value. In some cases, the function may have complex or undefined behavior at the limit point, making it challenging to determine the limit.
Some common techniques for computing limits include direct substitution, factoring, rationalization, and using limit laws. Other methods such as L'Hospital's rule and Taylor series expansions can also be used for more complex functions.
If a limit cannot be computed, it may indicate that the function has a discontinuity or an undefined behavior at the limit point. This can have significant implications for the function's behavior and may require further analysis or adjustments to the function.
Limits are used in various real-world applications, such as calculating the speed and acceleration of an object, determining the maximum or minimum value of a function, and analyzing the convergence of series. They are also essential in physics, engineering, and economics, among other fields.