The limit of the expression lim_{x -> ∞} (x/(x+1))^x can be evaluated using l'Hôpital's rule. The correct approach involves taking the natural logarithm of the expression, leading to ln(y) = lim_{x -> ∞} x * ln(x/(x+1)). This transforms the limit into a form suitable for applying l'Hôpital's rule, allowing for the evaluation of the limit as x approaches infinity. The final result confirms that the limit converges to a specific value.
PREREQUISITESStudents studying calculus, particularly those focusing on limits and indeterminate forms, as well as educators seeking to enhance their teaching methods in advanced mathematics.
Panphobia said:So I did e^whole statement with ln(x/(x+1))*x, after that I multiplied that expression by 1/x/1/x, then I go ln(x/(x+1)/1/x, I tried taking derivative of top and bottom but it doesn't help with finding an answer.
Panphobia said:Homework Statement
[itex]lim_{x -> \infty} \left( \frac{x}{x+1} \right) ^ {x}[/itex]
The Attempt at a Solution
So I did e^whole statement with ln(x/(x+1))*x, after that I multiplied that expression by 1/x/1/x, then I go ln(x/(x+1)/1/x, I tried taking derivative of top and bottom but it doesn't help with finding an answer.