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Finding Limits Algebraically quiz #1 Flashcards

Finding Limits Algebraically quiz #1
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  • How do you find the limit of a polynomial function as x approaches a given value?
    For a polynomial function, you can find the limit as x approaches a given value by direct substitution—simply plug the value of x into the function.
  • What steps should you take to find the limit of a rational function when direct substitution results in a zero denominator?
    If direct substitution gives a zero denominator, factor both the numerator and denominator, cancel any common factors, and then substitute the value to find the limit.
  • How do you find the limit of a rational function involving radicals when substitution gives a zero denominator?
    Multiply the numerator and denominator by the conjugate of the radical expression, simplify to cancel common factors, and then substitute the value to find the limit.
  • What is the limit of (x^2 + 2x - 15)/(x - 3) as x approaches 3?
    First, factor the numerator to (x - 3)(x + 5), cancel the (x - 3) terms, and substitute x = 3 into the remaining expression to get 3 + 5 = 8.
  • How do you find the limit of a polynomial function as x approaches a given value?
    You use direct substitution by plugging the value of x into the polynomial function to find the limit.
  • What should you do first when finding the limit of a rational function if direct substitution gives a zero denominator?
    You should factor both the numerator and denominator, cancel any common factors, and then substitute the value to find the limit.
  • What is the process for finding the limit of a rational function involving radicals when substitution gives a zero denominator?
    Multiply the numerator and denominator by the conjugate of the radical expression, simplify to cancel common factors, and then substitute the value to find the limit.
  • What is the limit of (x^2 + 2x - 15)/(x - 3) as x approaches 3?
    First, factor the numerator to (x - 3)(x + 5), cancel the (x - 3) terms, and substitute x = 3 into the remaining expression to get 8.
  • Why is it important to check the denominator when finding the limit of a rational function using direct substitution?
    If the denominator equals zero, direct substitution is not valid and you must use factoring or the conjugate method to simplify before evaluating the limit.
  • What is the purpose of multiplying by the conjugate when finding limits involving radicals?
    Multiplying by the conjugate helps eliminate the radical and creates a common factor that can be canceled, allowing you to evaluate the limit.