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Evaluating limits worksheets Grade 12

Evaluate limits by substitution, factoring, and comparing highest powers.

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Free · Worked example · 22 problems · Answer key · US Letter

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How to do it

Put the number in. If you get 0/0, factor and cancel first. As x → ∞, compare the highest powers.

lim⁡x→1−x2+x+2=2\lim_{x \to 1}-x^{2} + x + 2 = 2
−(1)2+(1)+2=2-(1)^{2} + (1) + 2 = 2a polynomial: put the number in

Example problems

  1. lim⁡x→−4x2+5x+4x+4=\lim_{x \to -4}\dfrac{x^{2} + 5x + 4}{x + 4} =
  2. lim⁡x→∞3x−5x−6=\lim_{x \to \infty }\dfrac{3x - 5}{x - 6} =
  3. lim⁡x→∞−9x−25x2−9x=\lim_{x \to \infty }\dfrac{-9x - 2}{5x^{2} - 9x} =
  4. lim⁡x→∞x+99x2+3x−7=\lim_{x \to \infty }\dfrac{x + 9}{9x^{2} + 3x - 7} =

Limits and derivatives

  1. Evaluating limits
  2. The power rule for derivatives
  3. The product rule
  4. The quotient rule
  5. The chain rule
  6. Derivatives of trig, exponential and log functions
  7. Equation of a tangent line
  8. Derivatives as rates of change
  9. Finding maximum and minimum points