Question

What is the limit as x approaches infinity of (ln(x+2)-ln(x+1))?

Answer 1

\[\ln\left(\dfrac{x+2}{x+1}\right)\]\[= \ln \left(1 + \frac{1}{x+1}\right)\]Does that ring a bell? :)

Answer 2

Before you go ahead and answer the question, you must see whether the logarithmic function exist or not.
By setting the function within the log to greater than 0.
e.g
x + 2 > 0 etc

In this question it does ^^

Answer 3

The \[\lim_{x \rightarrow \infty} (\ln(x+2)-\ln(x+1))\]
The value for x is 0 as it approaches infinity in this question.
Why?

As you substitute the value of infinity into this question, large values inside of a logarithmic over a large value in a logarithmic, is almost zero. So essential it is 0