The image shows the mathematical expression:

$\lim_{x \to 1} \frac{1}{x} = 1$

This statement is false. Let's analyze it:

The limit expression $\lim_{x \to 1} \frac{1}{x}$ means we are looking at the behavior of the function $f(x) = \frac{1}{x}$ as $x$ approaches 1. Evaluating $\frac{1}{x}$ at $x = 1$ gives:

$\frac{1}{1} = 1$

So, the value of the function is indeed 1 at $x = 1$, but this does not mean the limit equals 1 in general. The limit only asks how the function behaves as $x$ gets arbitrarily close to 1, which in this case it does tend to 1. Therefore, the limit is indeed 1.

In conclusion, while the limit calculation is correct, the overall equality $\lim_{x \to 1} \frac{1}{x} = 1$ is only valid under this context.

Would you like further clarification on this, or any additional details?

Here are 5 related questions:

1. What is the formal definition of a limit?
2. How do limits behave near discontinuities?
3. Can limits exist for functions with vertical asymptotes?
4. How do you compute limits that approach infinity?
5. How does L'Hopital's Rule apply to indeterminate forms in limits?

Tip: Always substitute the value directly into the limit expression to check for any potential discontinuities before drawing conclusions.