How do you find the Limit of #ln(x+1)/x # as x approaches infinity?
1 Answer
Jul 22, 2016
Explanation:
This limit is indeterminate because direct substitution yields
Therefore, we can apply L'Hospital's rule, which basically is taking a derivative of the numerator and the denominator at the same time.
Applying L'Hospital's rule gives us
This makes sense because if we look at the graph of our original function, we can see that as
graph{ln(x+1)/(x) [-10, 10, -5, 5]}