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Evaluating Limits Algebraically (Calculus I)

Free printable university Calculus I worksheet: evaluating limits by direct substitution, factoring and rationalising, and recognising the indeterminate form 0/0. Every limit verified numerically.

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Calculus I · Math worksheet
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Evaluating Limits Algebraically

Evaluate each limit. Try direct substitution first; if it gives the indeterminate form 0/0, simplify before substituting: factor and cancel, or multiply by the conjugate to rationalise a square root.

  1. 1.
    Evaluate: lim (x -> -3) of (2x^2 - 5x) / (x - 4)
  2. 2.
    Evaluate: lim (x -> 2) of (x2x^{2} - 2) / (x)
  3. 3.
    Evaluate: lim (x -> 0) of (-x2x^{2} + 3x + 3) / (x - 3)
  4. 4.
    Evaluate: lim (x -> 1) of (-3x^2 - x + 4) / (x - 1)
  5. 5.
    Evaluate: lim (x -> -3) of (2x^2 + 7x + 3) / (x2x^{2} + 5x + 6)
  6. 6.
    Evaluate: lim (x -> 1) of (-x2x^{2} + 4x - 3) / (x - 1)
  7. 7.
    Evaluate: lim (x -> 0) of (3x^2 + 4x) / (x2x^{2} + 2x)
  8. 8.
    Evaluate: lim (x -> 8) of (x−4\sqrt{x - 4} - 2) / (x - 8)
  9. 9.
    Evaluate: lim (x -> 7) of (x+18\sqrt{x + 18} - 5) / (x - 7)
  10. 10.
    Evaluate: lim (x -> 6) of (x+10\sqrt{x + 10} - 4) / (x - 6)
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