Limit without using de l'hopital

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

In summary, the limit without using de l'hopital is a mathematical technique for solving limits of functions without relying on L'Hopital's rule. It can be used when the function does not meet the conditions for applying L'Hopital's rule and other limit theorems, such as the Squeeze theorem or Trigonometric limit theorem, can be used instead. However, L'Hopital's rule may sometimes be a simpler and more efficient option. To ensure correct evaluation, the limit value can be plugged into the original function or compared with the graph near the limit value.

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.

1. What is the limit without using de l'hopital?

The limit without using de l'hopital is a mathematical technique used to solve limits of functions without using the L'Hopital's rule. It involves manipulating the expression algebraically or using other limit theorems to evaluate the limit.

2. When should I use the limit without using de l'hopital?

The limit without using de l'hopital should be used when the function does not satisfy the conditions for applying L'Hopital's rule, such as when the limit is in indeterminate form 0/0 or ∞/∞.

3. What are the other limit theorems that can be used instead of de l'hopital?

Some of the other limit theorems that can be used to evaluate limits without using de l'hopital include the Squeeze theorem, the Sandwich theorem, and the Trigonometric limit theorem.

4. Is the limit without using de l'hopital always a better option?

No, the limit without using de l'hopital may not always be a better option. In some cases, applying L'Hopital's rule may provide a simpler and more efficient solution. It is important to carefully consider the function and the given limits before choosing which method to use.

5. How do I know if I have correctly evaluated the limit without using de l'hopital?

You can verify the correctness of your evaluation by plugging in the limit value into the original function and seeing if it results in a valid output. You can also use graphing or a calculator to compare your result with the graph of the function near the limit value.