The problem asks to evaluate the limit:

$\lim_{x \to 0} \sec(x)$

Solution:

The secant function is defined as: $\sec(x) = \frac{1}{\cos(x)}.$

As $x \to 0$, the cosine of $x$ approaches 1: $\cos(0) = 1.$

Thus: $\sec(0) = \frac{1}{\cos(0)} = \frac{1}{1} = 1.$

Final Answer:

$\lim_{x \to 0} \sec(x) = 1.$

Would you like more explanation or have questions about the secant function?

Here are 5 related questions for practice:

1. What is $\lim_{x \to \pi/2^-} \sec(x)$?
2. What happens to $\sec(x)$ as $x \to \pi/2^+$?
3. Evaluate $\lim_{x \to 0} \tan(x)$.
4. Find the value of $\sec^2(x)$ when $x = \pi/4$.
5. Solve $\lim_{x \to \infty} \sec(x)$, assuming $x$ is constrained to even multiples of $\pi$.

Tip: Remember that $\sec(x)$ is undefined wherever $\cos(x) = 0$, such as $x = \pi/2, 3\pi/2, \dots$.