Indeterminate Form

Calculus Level pending

Evaluate the following limit to three decimal places.

$\large \displaystyle \lim_{ x \to \infty} \left[\ln(x-2)-\ln(x/2) \right]$

The answer is 0.693.

1 solution

Hobart Pao
May 25, 2016

$y = \displaystyle \lim_{x \to \infty} \ln \left( \dfrac{2 (x-2)}{x} \right)$ $e^y = \displaystyle \lim_{x \to \infty} \dfrac{2 (x-2)}{x}$ $e^ y = 2$ $y = \ln 2 \approx \boxed{0.693 }$

Indeterminate Form

The answer is 0.693.

1 solution

0 pending reports