Module limits 

Limit evaluation for mathematical expressions.

This module provides functions for computing limits of expressions as a variable approaches a specific value.

Overview

The limit module supports:

• Direct substitution for continuous functions
• Detection of indeterminate forms (0/0, ∞/∞, etc.)
• Limits at infinity
• One-sided limits (left and right)
• Common special limits (sin(x)/x, etc.)

Examples

Direct Substitution

use thales::limits::{limit, LimitPoint};
use thales::parser::parse_expression;

// lim_{x->2} x^2 = 4
let expr = parse_expression("x^2").unwrap();
let result = limit(&expr, "x", LimitPoint::Value(2.0));
// Returns Ok with value 4.0

Limit at Infinity

use thales::limits::{limit, LimitPoint};
use thales::parser::parse_expression;

// lim_{x->∞} 1/x = 0
let expr = parse_expression("1/x").unwrap();
let result = limit(&expr, "x", LimitPoint::PositiveInfinity);

Enums

IndeterminateForm

Types of indeterminate forms.

LimitError

Error type for limit evaluation failures.

LimitPoint

The point that a limit approaches.

LimitResult

Result of a limit evaluation.

Functions

limit

Evaluate the limit of an expression.

limit_left

Evaluate limit from the left (approaching from below).

limit_right

Evaluate limit from the right (approaching from above).

limit_with_lhopital

Evaluate the limit using L’Hôpital’s rule when needed.