The expression in your image appears to be:

$\lim_{{x \to 0}} \frac{x}{\tan x}$

To solve this limit, we can apply the following known limit property:

$\lim_{{x \to 0}} \frac{x}{\tan x} = 1$

This result holds because, for small values of $x$, the function $\tan x$ behaves similarly to $x$, meaning their ratio approaches 1 as $x \to 0$.

Therefore, the value of the limit is:

$\lim_{{x \to 0}} \frac{x}{\tan x} = 1$

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. What are some basic trigonometric limit properties?
2. How can L'Hopital's rule be applied to this limit?
3. How does the small-angle approximation for trigonometric functions help in solving limits?
4. What is the derivative of $\tan(x)$, and how does it relate to this limit?
5. How does this limit compare to other standard limits, such as $\lim_{x \to 0} \frac{\sin x}{x}$?

Tip: When dealing with trigonometric limits around 0, small-angle approximations can be very useful to simplify calculations.