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Find the limit or show that it does not exist.
$ \displaystyle \lim_{x \to \infty} \bigl[\ln (2 + x) - \ln (1 + x) \bigr] $
0
Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 6
Limits at Infinity: Horizontal Asymptotes
Limits
Derivatives
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
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his problem. Number forty two of this tour Calculus a fish in section two point six. Find the limit or show that it does not exist and the limit is well in this X approaches Infinity of Ellen of the quantity to six minus Alan with quantity one No sex. First, we use a property of natural locks to combine the two natural logs. Since it is a difference of natural longs Ah, oui. Interpret this as a ah quotient of the arguments to plus X in the numerator over one plus x of the developed later king. Now we use the property of limits. Teo Ah, we write this as instead of limited Ellen of this function since they function within a function limits allows us to bring in the limit inside of this function and instep do that naturally of the limit is expression infinity at this corner to politics over on politics. Now what we do inside of this Lim is that right? Each term, Brax. So it is easy to identify which terms will vanish to divide backs. Plus X rex is one. You're out of pride. Quantity one Rex, the six of Rex is one as experts is infinity. Each of these terms to Iraq's and one Iraq's vanishes. Zero. We're left with a fraction of one over one, which is torn, and our limit be equal to the natural log of one which is equal to zero. So the answer to our original limit is that the solution gives us a limit of zero. Is it a monster?
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