- #1
mousesgr
- 31
- 0
1. lim [(1+x)^(1/x) - e ] / x
x ->0
2. lim [sin(2/x)+cos(1/x)]^x
x -> inf
help...
x ->0
2. lim [sin(2/x)+cos(1/x)]^x
x -> inf
help...
Last edited:
#1 is in form 0 / 0.mousesgr said:qs 1 is not 0/0 or inf/inf from
how do consider L'Hopital's rule?
L'Hopital's rule is a mathematical concept that allows us to find the limit of a function when the limit of the numerator and denominator both approach zero or infinity. It states that if we have a fraction where both the numerator and denominator approach zero or infinity, then the limit of the fraction is equal to the limit of the derivative of the numerator divided by the derivative of the denominator.
L'Hopital's rule should only be used when we have a limit that is in an indeterminate form, such as 0/0 or ∞/∞. It cannot be used for limits that are already in a determinate form, such as 3/5 or ∞/2.
The steps for using L'Hopital's rule are:
Yes, there are limitations to using L'Hopital's rule. It can only be used for limits that are in an indeterminate form, and it may not always result in the correct answer. It is also important to note that the rule only applies to certain types of functions, such as rational functions.
Yes, L'Hopital's rule can be used for limits involving trigonometric functions. However, we must first convert the trigonometric functions into their equivalent exponential form before applying the rule.