---
title: "Computing Basic Limits - Direct Substitution"
slug: computing-basic-limits-direct-substitution
type: evergreen
stime: 2025-01-15 @ 12:00AM
status: evergreen
certainty: certain
importance: 5
tags: [calculus, limits]
---

The easiest way to evaluate a limit is to directly plug in the value of $x$.

**Example:**

$$
\lim_{x \to 1} (3x + 2)
$$

- Plug in $x = 1$: $3(1) + 2 = 5$

Since there's no division by zero or undefined behavior, the limit is just the function value at that point.

This method works when the function is continuous at the point you're approaching.

## Related

- [Notation of a Limit](notation-of-a-limit.md)
- [When a Limit Exists](when-a-limit-exists.md)
- [Computing Limits with Algebraic Simplification](computing-limits-with-algebraic-simplification.md)
- [Limit with Absolute Value - Jump Discontinuity](limit-with-absolute-value-jump-discontinuity.md)
- [Limit with Difference of Cubes](limit-with-difference-of-cubes.md)
- [Differential Calculus](differential-calculus.md)
- [Limit with Absolute Value - Piecewise Behavior](limit-with-absolute-value-piecewise-behavior.md)
- [Function Notation](function-notation.md)
- [Definition of Absolute Value](definition-of-absolute-value.md)
- [Absolute Value as Piecewise Function](absolute-value-as-piecewise-function.md)