The concept of a **limit** in mathematics, particularly in calculus, describes the value that a function or sequence approaches as the input approaches some value.

### Limit of a Function:
For a function \( f(x) \), the limit is written as:

\[
\lim_{{x \to a}} f(x)
\]

This reads as "the limit of \( f(x) \) as \( x \) approaches \( a \)." It represents the value that \( f(x) \) gets closer to as \( x \) gets closer to \( a \), without necessarily reaching \( a \).

#### Example:
\[
\lim_{{x \to 2}} (3x + 1)
\]

To solve:
\[
\lim_{{x \to 2}} (3x + 1) = 3(2) + 1 = 7
\]

### Limit at Infinity:
Sometimes, we are interested in the behavior of a function as \( x \) approaches infinity. For example:

\[
\lim_{{x \to \infty}} \frac{1}{x} = 0
\]

As \( x \) gets larger and larger, \( \frac{1}{x} \) gets closer to 0.

### Types of Limits:
1. **Finite Limit**: The function approaches a specific finite value as \( x \) approaches some value.
2. **Infinite Limit**: The

Explore the concept of limits in calculus with a focus on how functions approach values as inputs near a certain point or infinity. This page covers key formulas, including the limit of a function and limit at infinity, with examples such as \( \lim_{{x \to 2}} (3x + 1) \). Suitable for high school students in Grades 11-12.

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