L'Hospital's rule to find limits

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In summary, the student is asking for help with finding the limit of lnxtan(pix/2) as x approaches 1 from the right, using L'Hospital's rule. They have attempted the problem twice, getting the correct answer when arranging the ratio as lnx/1/tan(pix/2) but not getting any answer when arranging it as tan(pix/2)/1/lnx. They are wondering if this is because infinity/infinity is not a valid answer.
  • #1
MathewsMD
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Homework Statement


Find the limit, using L'Hospital's rule, if appropriate.
lim lnxtan(pix/2)
x->1^+

Homework Equations


The Attempt at a Solution


http://imgur.com/gbhQutU

I've done this question and gotten the correct answer by making lnx the numerator and 1/tan(pix/2) the denominator, but get the wrong answer when I make tan(pix/2) the numerator and 1/lnx the denominator. Is this because you cannot have -infinity/infinity? My solution is posted, and any help on where I went wrong or what steps to take would be very helpful.
 

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  • #2
Disregard.
 
  • #3
MathewsMD said:

Homework Statement


Find the limit, using L'Hospital's rule, if appropriate.
lim lnxtan(pix/2)
x->1^+

Homework Equations


The Attempt at a Solution


http://imgur.com/gbhQutU

I've done this question and gotten the correct answer by making lnx the numerator and 1/tan(pix/2) the denominator, but get the wrong answer when I make tan(pix/2) the numerator and 1/lnx the denominator. Is this because you cannot have -infinity/infinity? My solution is posted, and any help on where I went wrong or what steps to take would be very helpful.

You didn't do anything wrong in the second attempt, but sometimes one way of arranging the ratio for l'Hospital's gives you an easy solution and another way doesn't lead anywhere. The second attempt is just giving you more infinity/infinity type limits. You aren't getting a wrong answer, you just aren't getting any answer that's not still indeterminant. That's why it's worth thinking about alternatives before you start.
 
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FAQ: L'Hospital's rule to find limits

1. What is L'Hospital's rule?

L'Hospital's rule is a mathematical technique used to find the limit of a function that is in an indeterminate form, such as 0/0 or ∞/∞. It is also known as the rule of de l'Hospital or the rule of Bernoulli.

2. When should L'Hospital's rule be used?

L'Hospital's rule should be used when the direct substitution of the limit value into the function results in an indeterminate form. It is also used when traditional algebraic methods, such as factoring or simplifying, are not applicable.

3. How does L'Hospital's rule work?

L'Hospital's rule involves taking the derivative of both the numerator and denominator of the original function and then evaluating the limit again. This process can be repeated until a non-indeterminate form is obtained, or until it is determined that the limit does not exist.

4. Are there any restrictions on using L'Hospital's rule?

Yes, there are a few restrictions on using L'Hospital's rule. The function must be differentiable in a neighborhood of the limit point, and the limit must be in an indeterminate form that can be rewritten in the form of 0/0 or ∞/∞. Also, the limit must exist in order for L'Hospital's rule to be applicable.

5. What is the process for using L'Hospital's rule?

The process for using L'Hospital's rule involves taking the derivative of both the numerator and denominator of the original function, evaluating the limit again, and repeating this process until a non-indeterminate form is obtained. It is important to note that each time the limit is evaluated, the original function must be used, and not the derivative.

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