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Finding Limits Algebraically definitions

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  • Direct Substitution
    A method where the input value is plugged directly into the function to find the limit, valid when the function is defined at that point.
  • Polynomial
    An algebraic expression consisting of terms with non-negative integer exponents, allowing straightforward limit evaluation.
  • Root Function
    A function involving radicals, such as square roots, where limits can often be found by direct substitution if defined.
  • Rational Function
    A function expressed as the ratio of two polynomials, requiring denominator analysis when finding limits.
  • Denominator
    The bottom part of a fraction, whose value determines if direct substitution is possible when finding limits.
  • Factoring
    The process of rewriting an expression as a product of simpler expressions, used to simplify rational functions for limits.
  • Common Factor
    An expression present in both numerator and denominator, which can be canceled to resolve indeterminate forms in limits.
  • Conjugate
    An expression formed by changing the sign between two terms, used to simplify limits involving radicals.
  • Indeterminate Form
    An expression like 0/0 encountered during substitution, signaling the need for algebraic manipulation to find the limit.
  • Numerator
    The top part of a fraction, which may be manipulated along with the denominator to simplify limit expressions.
  • Radical
    A mathematical symbol indicating a root, often complicating direct substitution in limit problems.
  • Cancellation
    The process of removing a common factor from numerator and denominator, allowing further simplification of a limit.
  • Table of Values
    A list of input-output pairs used to estimate limits numerically, often replaced by algebraic methods for efficiency.
  • Graph
    A visual representation of a function, sometimes used to estimate limits but not always necessary with algebraic techniques.
  • Limit Value
    The number a function approaches as the input approaches a specific point, found using algebraic strategies.