Limit gives indeterminate form

Thread starter jog511
Start date Aug 30, 2014
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Form Limit

In summary, an indeterminate form in limits refers to a situation where the limit of a function cannot be determined by simply evaluating the function at the given point. This can happen when the function approaches a particular value or expression that is undefined or cannot be represented by a simple numerical value. Indeterminate forms can occur due to several reasons, including division by zero, taking the square root of a negative number, or when the function approaches a vertical asymptote. These situations result in undefined or infinite numbers, making it impossible to determine the limit of the function. However, indeterminate forms can be solved using mathematical techniques such as L'Hôpital's rule, which involves taking the derivative of both the numerator and denominator of the function and then evaluating

Aug 30, 2014

jog511

Homework Statement

limx->∞ e^5x/ln(2x)

Homework Equations

The Attempt at a Solution

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Aug 30, 2014

jackarms

Well, what work have you done so far with the limit? It's not enough here on PF to simply give the problem statement and nothing else.

FAQ: Limit gives indeterminate form

What is an indeterminate form in limits?

An indeterminate form in limits refers to a situation where the limit of a function cannot be determined by simply evaluating the function at the given point. This can happen when the function approaches a particular value or expression that is undefined or cannot be represented by a simple numerical value.

How do you know if a limit gives an indeterminate form?

A limit gives an indeterminate form if, after evaluating the function at the given point, the result is something that cannot be represented by a single numerical value. Common examples include 0/0, ∞/∞, and ∞-∞.

What causes a limit to give an indeterminate form?

Indeterminate forms can occur due to several reasons, including division by zero, taking the square root of a negative number, or when the function approaches a vertical asymptote. These situations result in undefined or infinite numbers, making it impossible to determine the limit of the function.

Can indeterminate forms be solved?

Yes, indeterminate forms can be solved by using mathematical techniques such as L'Hôpital's rule, which involves taking the derivative of both the numerator and denominator of the function and then evaluating the limit again. This process can be repeated until a single numerical value is obtained.

Why are indeterminate forms important in calculus?

Indeterminate forms are important in calculus because they represent situations where the limit of a function cannot be determined by conventional methods. By using techniques such as L'Hôpital's rule, we can solve these forms and find the limit of the function, allowing us to better understand the behavior of functions and make accurate predictions in real-world applications.