The first derivative of (1) = lim [(4n+1)/(6n+1)]' is still ∞ /∞.

Second derivative =lim[4/6]=2/3

(2) First derivative =lim[(2x+ 1)/(3x? )]' Or ∞ /∞

Second derivative =lim[2/6x]=0

This problem requires a direct L 'Bida law, which can be deduced up and down. 0/0 or ∞ /∞ can use the Lobida rule.

Extended data:

Finding the limit is one of the important contents and the basic part of higher mathematics, so it is of great significance to master the method of finding the limit skillfully. Robida's law is used to find the fractional limit of numerator and denominator approaching zero.

(1) Before starting to find the limit, check whether it is met? Type configuration, otherwise the abuse of L'H?pital's law will be wrong (in fact, the formal numerator does not need infinity, and the denominator can be infinite). When it does not exist (excluding the situation), it cannot be used. At this time, it is said that L'H?pital's law is not applicable, and other methods should be used to find the limit. For example, use Taylor formula to solve.

If the conditions are met, L'H?pital's law can be used repeatedly until the limit is found? .

(3) L'H?pital's law is an effective tool to find the limit of indeterminate form, but if only L'H?pital's law is used, the calculation will be very complicated, and other methods must be combined, such as separating the product factor of non-zero limit in time to simplify the calculation, replacing the product factor with equivalent quantity, and so on? .

⑷ Robida's law is often used to find the limit of infinitives. Basic infinitive limit: type; Type (or), and the limits of other forms, such as type, type, and type, type and type, can be solved by transforming into the above two basic infinitive forms.

References:

Infinity (Mathematics) _ Baidu Encyclopedia?