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Finding Limits Algebraically definitions

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  • Direct Substitution
    A method where the value of x is plugged directly into a 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, often allowing limits to be found by direct substitution.
  • Rational Function
    A function expressed as the ratio of two polynomials, where limit evaluation depends on the denominator's value at the point of interest.
  • Denominator
    The bottom part of a fraction in a rational function, whose value at a specific x determines if direct substitution is possible.
  • Numerator
    The top part of a fraction in a rational function, often factored to cancel with the denominator when finding limits.
  • Common Factor
    An algebraic term present in both the numerator and denominator, which can be canceled to simplify limit evaluation.
  • Factoring
    The process of rewriting an expression as a product of simpler expressions, used to simplify rational functions when the denominator is zero.
  • Radical
    An expression involving a root, such as a square root, which may require special techniques for limit evaluation.
  • Conjugate
    A binomial formed by changing the sign between two terms, used to eliminate radicals in denominators or numerators.
  • Indeterminate Form
    A situation, such as 0/0, where direct substitution does not yield a clear limit, requiring further algebraic manipulation.
  • Limit
    The value a function approaches as the input approaches a specific point, foundational to calculus and continuity.
  • Basic Root Function
    A function involving a root, like a square root, where limits can often be found by direct substitution if defined.
  • Table of Values
    A list of input-output pairs used to estimate limits numerically when algebraic methods are not straightforward.
  • Graphical Approach
    A visual method for estimating limits by observing the behavior of a function near a specific point.
  • Cancellation
    The process of removing a common factor from the numerator and denominator to simplify a function before evaluating a limit.