- #1
Nope
- 100
- 0
Homework Statement
lim x->0
5x(cos 9x-1)/sin 5x-5x
Homework Equations
The Attempt at a Solution
answer is 243/25
The derivative of sin 5x-5x is always 0,
dunno know how to do it...
Inirit said:You'd use the rule if you got a 0 in the denominator after plugging in the limit of x, not if it were 0 to begin with. An equation over 0 would always be over 0 no matter how many times you differentiate it.
Deadstar said:Edit: Actually I think you meant if you differentiate zero you get zero...
Nope said:I differentiated like 5 times, I still got 0..
I notice that there is always a x*cos(9x) in the nominator...which make whole thing equal to 0..
L'Hopital's Rule is a mathematical technique used to evaluate limits involving indeterminate forms. It can be used when the numerator and denominator of a fraction both approach 0 or ∞, or when the limit of a function involves an undefined expression such as 0/0 or ∞/∞.
L'Hopital's Rule states that if the limit of a function f(x)/g(x) is an indeterminate form, then the limit of the derivative of f(x) divided by the derivative of g(x) will be the same as the original limit. In other words, we can solve the limit by taking the derivatives of both the numerator and denominator and evaluating the new fraction.
No, L'Hopital's Rule can only be used when the limit of a function is in indeterminate form. If the limit is not in indeterminate form, then the rule cannot be applied.
One common mistake is using the rule when it is not applicable, as mentioned in the previous question. Another mistake is not simplifying the new fraction after taking the derivatives, which can lead to incorrect results. It is also important to check that the derivatives exist at the point where the limit is being evaluated.
No, L'Hopital's Rule is specifically used to evaluate limits involving indeterminate forms. It cannot be used to solve other types of problems, such as finding the minimum or maximum value of a function.