The expression shown in the image is:

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

To solve this limit:

1. Direct Substitution: Substituting $x = 0$ directly into the expression $\frac{\tan x}{x}$ results in an indeterminate form $\frac{0}{0}$.

2. Using Limit Identity: There's a well-known trigonometric limit identity:

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

Thus, the value of the limit is:

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

Would you like further details or explanations about how this result is derived?

Here are 5 related questions to explore:

1. How do you compute limits involving other trigonometric functions?
2. Why is L'Hôpital's Rule useful for indeterminate forms like $\frac{0}{0}$?
3. What is the difference between the limit of $\frac{\sin x}{x}$ and $\frac{\tan x}{x}$ as $x \to 0$?
4. How can you evaluate limits of functions using series expansion?
5. What other common limit identities should be memorized for calculus?

Tip: When faced with indeterminate forms like $\frac{0}{0}$, try using limit identities or L'Hôpital’s Rule for a solution.