Question

For what value of 'a' is the following equation true?

\[\lim_{x \rightarrow \infty} (\frac{x + a}{x - a})^{x} = e\]

Answer 1

i am going to make a guess, that \(a=\frac{1}{2}\) but i could be wrong
i think you need to find the limit, which will be \(e^{f(a)}\) and then set \(f(a)=1\)

Answer 2

form as it is gives \(1^{\infty}\)
you can use l'hopital to find the limit