The limit of the expression x*cot(x) - 1/x^2 as x approaches 0 evaluates to 0. The discussion highlights that applying L'Hôpital's rule may not yield straightforward results due to the indeterminate form. Instead, substituting cot(x) with cos(x)/sin(x) and expanding the functions using power series for sin(x) and cos(x) provides a clearer path to the solution. The key takeaway is that deeper function expansion is necessary to resolve the limit correctly.
PREREQUISITESStudents and educators in calculus, particularly those focusing on limits and trigonometric functions, as well as anyone seeking to improve their problem-solving skills in advanced mathematics.
tsuwal said:Homework Statement
limit x*cot(x)-1/x^2
x->0
Homework Equations
lim x*cot(x)=1
x->0
The Attempt at a Solution
it's an indetermination but L'hopital rule doesn't help very much..
I assume you mean limit (x*cot(x)-1)/x2 as x->0.tsuwal said:limit x*cot(x)-1/x^2
x->0