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Jrlinton
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Homework Statement
Just quickly, can you apply l'hopital's rule when the limit is evaluated as undefined/undefined as in the following limit:
L'Hopital's Rule: Homework Statement
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In summary, L'Hopital's Rule is a theorem used to evaluate limits involving indeterminate forms. It can only be applied when the limit of a quotient of two functions is an indeterminate form, and it involves taking the derivative of the numerator and denominator separately. This rule can also be used for limits involving trigonometric functions, but it is important to ensure that the functions are in a differentiable form. Some common mistakes when using L'Hopital's Rule include applying it to non-indeterminate limits, not simplifying the resulting expression, and not checking for differentiability of the functions.
Just quickly, can you apply l'hopital's rule when the limit is evaluated as undefined/undefined as in the following limit:
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Ray Vickson
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Tell us what YOU think, first. Then, after seeing your work, we might be able to help.Jrlinton said:
1. What is L'Hopital's Rule?
L'Hopital's Rule is a mathematical theorem that is used to evaluate limits involving indeterminate forms, such as 0/0 or ∞/∞. It states that if the limit of a quotient of two functions is an indeterminate form, then the limit can be found by taking the derivative of the numerator and denominator separately and evaluating the resulting quotient.
2. When is L'Hopital's Rule applicable?
L'Hopital's Rule can only be used when the limit of a quotient of two functions is an indeterminate form. This typically occurs when both the numerator and denominator approach 0 or ∞, but it can also occur in other cases such as when the numerator approaches a finite value while the denominator goes to ∞. It is not applicable for limits involving other types of indeterminate forms, such as ∞ - ∞ or 0 x ∞.
3. How do you use L'Hopital's Rule?
To use L'Hopital's Rule, first determine if the limit of the quotient of two functions is an indeterminate form. If it is, take the derivative of the numerator and denominator separately. Then, evaluate the resulting quotient at the original limit value. If the limit is still an indeterminate form, repeat the process until a definitive answer is obtained.
4. Can L'Hopital's Rule be used for limits involving trigonometric functions?
Yes, L'Hopital's Rule can be used for limits involving trigonometric functions. However, the functions must be in a form that is compatible with taking derivatives. This may require using trigonometric identities to rewrite the function before applying L'Hopital's Rule.
5. What are some common mistakes when using L'Hopital's Rule?
One common mistake when using L'Hopital's Rule is applying it to a limit that is not an indeterminate form. This can lead to incorrect results. Additionally, care must be taken to ensure that the functions being used are differentiable at the limit point. Another mistake is not simplifying the resulting expression after taking the derivative, which can also lead to incorrect results.
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