Solving $\lim_{n\rightarrow \o}\frac{1}{x}^x$ Problem

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In summary, the problem is finding the limit as x approaches 0 of (1/x)^x and L'Hopital's rule can be used to solve it by rewriting it as ln(y) = xln(1/x) = -xln(x) and then applying L'Hopital's rule. The final answer is 1.
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Physicsisfun2005
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Not sure if there is and answer

[tex]\lim_{n\rightarrow \o}\frac{1}{x}^x[/tex]


i suck at latexing lol...liimit approaching zero from the right i think...and its (1/x)^x...the quantity to the x power.
...i don't think i can use L'Hopitals rule...so how do i solve it?
 
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(I assume it is x going to 0, not n!)

Sure you can use L'Hopital's rule. This is a (infinity)0 form so let y= (1/x)x. ln(y)= x ln(1/x)= -xln(x) and you can write that as [itex]-\frac{ln x}{\frac{1}{x}}[/itex]. Apply L'Hopital's rule to that. Whatever you get for ln y, the limit of the original problem is the exponential of that.
 
  • #3
i got 1 as my answer...is that right?
 
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FAQ: Solving $\lim_{n\rightarrow \o}\frac{1}{x}^x$ Problem

What is the definition of a limit?

A limit is a mathematical concept that describes the behavior of a function as the input value approaches a certain value. It is denoted by the notation "lim", followed by the variable approaching the value, and then the function.

How do you solve a limit problem?

To solve a limit problem, you can use algebraic manipulation, graphing, or numerical methods. Generally, you need to analyze the function and its behavior as the input value approaches the given value, and then use appropriate techniques to find the limit.

What is the limit of a function at infinity?

The limit of a function at infinity is the value that the function approaches as the input value gets larger and larger. It is also known as the limit at infinity or the infinite limit.

What is the Squeeze Theorem and how is it used to solve limit problems?

The Squeeze Theorem, also known as the Sandwich Theorem, states that if two functions have the same limit at a point, and a third function is always between them, then the third function also has the same limit at that point. This theorem is useful for solving limit problems by using a simpler function that is "sandwiched" between two more complex functions.

How do you solve a limit problem involving infinity?

To solve a limit problem involving infinity, you can use specific techniques such as L'Hopital's Rule, or you can rewrite the function in a way that allows you to evaluate the limit as the input value approaches infinity. It is also important to consider the behavior of the function as the input value gets infinitely large.

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