Linear Approximation Calculator
Estimate a function value near a known point using its tangent line. Choose a function, enter the base point and nearby x-value, and get a clear step-by-step solution instantly.
Enter approximation values
Result
Enter values and click calculate.
Choose a nearby point
Linear approximation works best when x is close to the base point a, where the function and derivative are easy to evaluate.
Use the tangent line
The tangent line at x = a has slope f′(a), so it provides a quick local estimate of the function.
Compare the error
The calculator also shows the actual function value and approximation error so you can judge the estimate.
Frequently asked questions
What is linear approximation?
Linear approximation estimates a function near a known point using the tangent line at that point.
When is the approximation accurate?
It is usually most accurate when x is very close to a and the function is smooth near the base point.
Are trigonometric inputs in radians?
Yes. Sine and cosine values use radians, which is standard in calculus.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
