- #1
catapax
- 6
- 0
how can i solve lim (1+2^1/x)/(3+2^1/x) without using de l'hopital?
catapax said:sorry for x→0±
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.
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 ∞/∞.
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.
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.
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.