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Linearization definitions

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  • Tangent Line
    A straight line that touches a curve at a single point and matches the curve's slope at that point.
  • Derivative
    A measure of how a function's output changes as its input changes, representing the slope at a specific point.
  • Point of Interest
    A specific input value near which a function is approximated by a line for easier calculations.
  • Linearization
    A process of approximating a function near a point by using the equation of its tangent line.
  • Linear Approximation
    An estimation method using a line to predict function values close to a chosen input.
  • Smooth Curve
    A graph with no sharp corners, allowing for accurate tangent line approximations at any point.
  • Equation of a Line
    A mathematical expression representing a straight path, often used to approximate curves locally.
  • Slope
    A value indicating the steepness of a line, given by the derivative at a specific point on a curve.
  • Output Value
    The result of evaluating a function at a particular input, often used in constructing approximations.
  • Approximation Region
    The interval around a chosen input where a function closely resembles its tangent line.
  • Accuracy
    A measure of how close an estimated value is to the actual function value, highest near the point of interest.
  • Power Rule
    A differentiation technique used to find the derivative of functions with variables raised to powers.
  • Function Value
    The output produced by substituting a specific input into a mathematical rule or formula.
  • Real-World Application
    A practical use of mathematical concepts, such as estimating complex function values in science or engineering.
  • Input Value
    A specific number substituted into a function to determine its corresponding output.