## anonymous one year ago What is the limit as x approaches infinity of (ln(x+2)-ln(x+1))?

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1. ParthKohli

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

2. anonymous

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 ^^

3. anonymous

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

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