Limit x to o: $\lim_{h\to 0}=-\frac{1}{5}$

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  • Thread starter karush
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In summary, "limit x to o" means approaching the value of 0 for the variable x. The purpose of taking the limit of a function is to understand its behavior as the input values get closer to a specific value. To solve for the limit of a function, we evaluate the function as the input values approach the specific value. The value -1/5 represents the limit of the function as the input values approach 0. The limit of a function can be different from the value of the function at a specific point, depending on the continuity and asymptotes of the function.
  • #1
karush
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$#46p60$
$$\lim_{{h}\to{0}}\frac{\frac{1}{5+h}-\frac{1}{5}}{h}=-\frac{1}{5}$$

Multiply numerator and denomator by $\frac{1}{h}$
$$\frac{-1}{5h+25}$$
$$h\to 0$$ thus $\frac{-1}{25}$

I hope anyway
 
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  • #2
Correct! Alternatively, you might recognize this as the derivative of 1/x evaluated at x = 5, i.e.

$\displaystyle \lim_{{h}\to{0}}\frac{\frac{1}{5+h}-\frac{1}{5}}{h} = \frac{d}{dx} \left(\frac{1}{x}\right)\bigg|_{x=5} = -\frac{1}{x^2}\bigg|_{x=5} = -\frac{1}{25}.$
 
  • #3
https://dl.orangedox.com/DllM3xBiyI8YRHbmhY
 

FAQ: Limit x to o: $\lim_{h\to 0}=-\frac{1}{5}$

1. What does "limit x to o" mean in this context?

In this context, "limit x to o" means that we are approaching the value of 0 for the variable x.

2. What is the purpose of taking the limit of a function?

The limit of a function helps us to understand the behavior of the function as the input values get closer and closer to a specific value. It can also help us to determine if a function is continuous at a certain point.

3. How do you solve for the limit of a function?

To solve for the limit of a function, we need to evaluate the function as the input values approach the specific value. If the function approaches a single value, then that value is the limit of the function. If the function has different values from the left and right sides, then the limit does not exist.

4. What does the value -1/5 represent in this limit?

The value -1/5 represents the limit of the function as the input values approach 0. It indicates that as the input values get closer and closer to 0, the function is approaching a value of -1/5.

5. Can the limit of a function be different from the value of the function at a specific point?

Yes, the limit of a function can be different from the value of the function at a specific point. This can happen if the function is not continuous at that point or if there is a vertical asymptote at that point. In this case, the limit represents the behavior of the function as the input values approach the specific point, while the value of the function at that point may be different.

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