Limit without using de l'hopital

Thread starter catapax
Start date Nov 28, 2012
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l'hopital Limit

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To solve the limit lim (1+2^(1/x))/(3+2^(1/x)) as x approaches 0 without using L'Hôpital's rule, one must analyze the behavior of 2^(1/x) as x approaches 0 from both the positive and negative sides. As x approaches 0 from the positive side, 2^(1/x) approaches infinity, while from the negative side, it approaches 0. This leads to different limit results: for x→0+, the limit evaluates to 1, and for x→0-, it evaluates to 1/3. Additionally, to simplify (2x+3)/(x+1) as x approaches 0, the limit can be directly computed as 3. The discussion emphasizes the importance of understanding limits through case analysis rather than relying solely on L'Hôpital's rule.

Nov 28, 2012

catapax

how can i solve lim (1+2^1/x)/(3+2^1/x) without using de l'hopital?

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Nov 28, 2012

catapax

sorry for x→0±

Nov 28, 2012

haruspex

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How would you simplify (2x+3)/(x+1)?

Nov 28, 2012

Dick

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catapax said:

sorry for x→0±

Split it into cases. What lim x->0+ of 2^(1/x)? What about lim x->0-? You should be able to tell just by thinking about it.

Nov 28, 2012

Mark44

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I'm locking this post as a courtesy to Dick and haruspex, because the OP showed no effort.

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