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Linear Approximation Formula Calculator
Linear approximation is crucial to many well-known numerical techniques, such as Euler’s Method, Ranga Kutta methods, etc. to approximate solutions to ordinary differential equations. The calculation is based on the closeness of the tangent line to the graph of the function around a point.
For a given point x0, if x0 is in the domain of the function f(x) i.e. the function is differentiable at that point, the equation of the graph of f(x) at the point (x0,y0) where y0=f(x0) becomes:
y-y0=f’(x0)(x-x0)
For any value x1 that is sufficiently close to x0, it can be said that x1=x0+Δx, where Δx is the difference between x1 and x0.
Consequently, the value of y1 is approximated by f(x0+Δx) on the tangent line, given by:
y1=y0+Δx*f’(x0)
where f’(x0) is the derivative of the function f(x) at the point x0.
For Δy=y1-y0, we obtain Δy=Δx*f’(x0). In the limit that x approaches x0, the final equation becomes:
L(x)≈f(x0)+f’(x)(x-x0)
where L(x) represents the linear approximation to the function f(x) at the point x0. The calculator will calculate linear approximation to the explicit curve at any given point.
Calculator Options
Function to approximate ()
X0 (a)
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References
This online resource may be cited as follows
MLA
"Quest Graph™ Linear Approximation Formula Calculator." AAT Bioquest, Inc., 11 Sep. 2026, https://www.aatbio.com/tools/linear-approximation-formula-calculator.
APA
AAT Bioquest, Inc. (2026, September 11). Quest Graph™ Linear Approximation Formula Calculator. AAT Bioquest. https://www.aatbio.com/tools/linear-approximation-formula-calculator.
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  • Enter a function into the box on the right with "x" as the independent variable. Round brackets have to be placed around "x" in accordance to the type and order of operation. For example, in the case of trigonometric functions, enter cos(x) and not cosx. In addition, the multiplication operator has to defined explicitly with "*" i.e. cos(2*x) and not cos(2x).
  • Enter a numeric value for x0. The calculator does not accept “pi”, so enter values in degrees when required and the calculator will convert it to radians accordingly. For example, to test linear approximation at a point “pi/2”, please enter “90”.
  • Verify that your function and point is accurate.
  • Press the "Calculate Linear Approximation" button to display results.