1. What is a Limit?

The limit of a function is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. The notation \(\lim_{x \to a} f(x) = L\) means that as x gets arbitrarily close to a, f(x) gets arbitrarily close to L.

2. How Does the Calculator Work?

The calculator evaluates the limit of a function using numerical approximation:

Where:

• \( f(x) \) — The function to evaluate
• \( a \) — The value x approaches
• \( L \) — The limit value (if it exists)

Explanation: The calculator approaches the limit point from both sides (unless specified) and checks for convergence.

3. Importance of Limits

Details: Limits are essential for defining derivatives, integrals, and continuity. They form the foundation of calculus and are used in physics, engineering, and economics.

4. Using the Calculator

Tips: Enter the function using standard mathematical notation (e.g., "x^2" for x squared, "sin(x)" for sine of x). Specify the approach value and direction (left, right, or both).

5. Frequently Asked Questions (FAQ)

Q1: What if the limit doesn't exist?
A: The calculator will indicate if the left and right limits disagree or if the function approaches infinity.

Q2: Can I calculate limits at infinity?
A: Yes, enter "inf" as the approach value for limits as x approaches infinity.

Q3: What functions are supported?
A: Most elementary functions: polynomials, trigonometric, exponential, logarithmic, etc.

Q4: How accurate are the results?
A: Results are numerically approximated. For exact solutions, symbolic computation is needed.

Q5: Can I use variables other than x?
A: Currently, the calculator only supports functions of x.