Limit Problem (L'hospitals rule ) (difference)

In summary, L'Hospital's rule is a mathematical concept used to evaluate limits of indeterminate forms, such as 0/0 or ∞/∞. It should be used when the limit cannot be determined through direct substitution and involves trigonometric functions, logarithms, or exponentials. The process of using L'Hospital's rule involves taking the derivative of both the numerator and denominator of the original function and evaluating the limit again, which can be repeated until the limit can be determined or the resulting expression is no longer indeterminate. Common mistakes when using L'Hospital's rule include not checking for indeterminate forms and not correctly taking the derivative or simplifying the resulting expression. However, there are limitations to this rule, such
  • #1
Seiya
43
1
Help please =P I've been doing all the l'hospitals rule problems fine and i did the limit of 1/x-cscx fine... same for otehers but i can't get this one??

lim x->infinity (x-ln[x])

I tried making x = 1/x^-1 and then combining them but that made it so confusing, is that the right approach?? :bugeye:

Any advice appreciated. Thank you!
 
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  • #2
Your approach works. Just make sure you separately differentiate the fraction in the numerator from the fraction in the denominator.
 

What is the limit problem (L'Hospital's rule)?

The limit problem, also known as L'Hospital's rule, is a mathematical concept used to evaluate limits of indeterminate forms. These are expressions where the limit cannot be determined through direct substitution and are often in the form of 0/0 or ∞/∞.

When should L'Hospital's rule be used?

L'Hospital's rule should be used when the limit of a function cannot be determined through direct substitution and is in an indeterminate form. It is also useful when the limit involves trigonometric functions, logarithms, or exponentials.

What is the process of using L'Hospital's rule?

The process of using L'Hospital's rule involves taking the derivative of both the numerator and denominator of the original function, then evaluating the limit again. This process can be repeated until the limit can be determined or until the resulting expression is no longer in an indeterminate form.

What are some common mistakes when using L'Hospital's rule?

One common mistake when using L'Hospital's rule is not checking if the limit is in an indeterminate form before applying the rule. Another mistake is not taking the derivative correctly or not simplifying the resulting expression before evaluating the limit again.

Are there any limitations to L'Hospital's rule?

Yes, there are limitations to L'Hospital's rule. It can only be used for limits involving indeterminate forms, and it may not always provide the correct answer. It is also important to note that L'Hospital's rule cannot be used for limits at infinity.

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