Solving Limit Problem: $x \to 0^{-}$ e^$\frac{1}{x}$

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In summary, we are trying to find the limit of $e^{\frac{1}{x}}$ as $x$ approaches $0$ from the left. Using the continuity property of limits, we can rewrite this as $e^{\lim_{x\to0^-}\frac{1}{x}}$. As $\frac{1}{x}$ approaches $-\infty$, the limit of $e^{\frac{1}{x}}$ becomes $e^{-\infty}$, which is equal to $0$. Therefore, the limit of $e^{\frac{1}{x}}$ as $x$ approaches $0$ from the left is $0$.
  • #1
tmt1
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$\d{x}{{0}^{-}} e ^ {\frac{1}{x}}$

I am trying to solve this limit.

Now, if we have $\lim{x}\to{0^{-}}1/x$ , doesn't it become $\infty$?
 
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  • #2
Are you trying to find the following limit?

\(\displaystyle L=\lim_{x\to0^{-}}e^{\frac{1}{x}}\)

If so, then you should note that:

\(\displaystyle \lim_{x\to0^{-}}\frac{1}{x}=-\infty\)

So, what does this tell you about $L$?
 
  • #3
hey there. (Wave)
perhaps you remember that $\lim_{{x}\to{a}}f(g(x))=f(\lim_{{x}\to{a}}g(x))$ this is the limit continuity property.

so start of with $\lim_{{x}\to{0^-}}\frac{1}{x}$ this goes to $-\infty$ (you can show intermediate steps if necessary)

what is $e^{-\infty}$? once you determine that, you have your answer :eek:
 
  • #4
Can't figure out how to edit my post to fix it. It's not under thread tools
 
  • #5
At the bottom next to "Reply with quote" it should say edit post. if not, there is a time cap to edit posts i believe so it's possible you may no longer be able to edit it.
 
  • #6
There is a 2 hour limit on editing the first post of a thread (which has now expired in this thread), and all other posts have a 24 hour limit.

You can just quote your first post, and then remove the quote tags and fix what you want to fix. :D
 

FAQ: Solving Limit Problem: $x \to 0^{-}$ e^$\frac{1}{x}$

What is a limit problem?

A limit problem refers to finding the value that a function approaches as the input approaches a specific point or value. In other words, it is finding the value of a function at a particular point or value that it cannot be evaluated at directly.

What is the limit of a function?

The limit of a function is the value that the function approaches as the input approaches a specific point or value. It is denoted by the symbol "lim" and is often used to describe the behavior of a function near a specific point or value.

How do you solve a limit problem?

To solve a limit problem, you can use various techniques such as substitution, factoring, and algebraic manipulation. It is also important to understand the properties of limits, such as the product, quotient, and power rules. In some cases, you may need to use L'Hopital's rule or graph the function to determine the limit.

What is the limit problem of $x \to 0^{-}$ e^$\frac{1}{x}$?

The limit problem of $x \to 0^{-}$ e^$\frac{1}{x}$ is asking for the value that this function approaches as x approaches 0 from the left side. In other words, we are trying to find the limit of the function as x gets closer and closer to 0 from the negative side.

What is the answer to the limit problem $x \to 0^{-}$ e^$\frac{1}{x}$?

The answer to this limit problem is 0. This is because as x approaches 0 from the negative side, the function e^$\frac{1}{x}$ approaches 0. This can be seen by graphing the function or using substitution to evaluate the limit.

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