Question

Determine the value of k = real such that:
limit (x -> infinity) ((X^2 + 1)^(0.5) - (x^2 + kx)^(0.5)) = 3

Answer 1

\[\lim_{x \rightarrow \infty} (\sqrt{x^2+1} - \sqrt {x^2+kx} ) = 3\]