Indeterminate limit of the form 1/0

Thread starter Zaurus21
Start date May 26, 2013
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In summary, an indeterminate limit of the form 1/0 is a mathematical expression in which the denominator approaches 0 while the numerator remains constant, resulting in an undefined value. These types of limits are important in evaluating complex functions and determining the behavior of a system. To solve an indeterminate limit of the form 1/0, advanced mathematical concepts such as L'Hôpital's rule or the squeeze theorem must be used. L'Hôpital's rule is a principle that allows us to find the limit of a fraction by taking the ratio of the derivatives of the numerator and denominator. An indeterminate limit of the form 1/0 cannot have a defined value, but its behavior and ultimate value can be determined using

May 26, 2013

Zaurus21

When finding lim(x->1) (1+2ln(x))^(1/(x-1)) = 1^(infinity) I let
y = (1+2ln(x))^(1/(x-1)) then ln both sides giving
ln(y) = ln(1+2ln(x)))/(x-1)
Taking the limit of ln(y) gives 1/0, which is indeterminate and hence the limit does not exist.
However, I typed this into MS Mathematics and got the limit as e^2.
Help please.

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May 26, 2013

Zaurus21

I made an arithmetic error. Nevermind.

FAQ: Indeterminate limit of the form 1/0

What is an indeterminate limit of the form 1/0?

An indeterminate limit of the form 1/0 is a mathematical expression in which the denominator is approaching 0 while the numerator remains constant. This results in an undefined value, also known as an indeterminate form.

Why is an indeterminate limit of the form 1/0 important?

Indeterminate limits of the form 1/0 are important because they represent situations in which the outcome is uncertain or undefined. In mathematics, these types of limits are often used to evaluate complex functions and to determine the behavior of a system.

How do you solve an indeterminate limit of the form 1/0?

An indeterminate limit of the form 1/0 cannot be solved using simple algebraic techniques. Instead, it requires the use of advanced mathematical concepts such as L'Hôpital's rule or the squeeze theorem.

What is L'Hôpital's rule?

L'Hôpital's rule is a mathematical principle used to evaluate indeterminate limits, including those of the form 1/0. It states that the limit of a fraction can be found by taking the ratio of the derivatives of the numerator and denominator as the independent variable approaches the limit point.

Can an indeterminate limit of the form 1/0 have a defined value?

No, an indeterminate limit of the form 1/0 does not have a defined value. This is because the denominator is approaching 0, resulting in an undefined or infinite value. However, by using L'Hôpital's rule or other mathematical techniques, we can determine the behavior of the limit and its ultimate value.