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Mathematics · Grades 11–12

Limits of polynomials

Polynomials are continuous at every real input, so direct substitution applies.

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The key idea

Polynomials are continuous at every real input, so direct substitution applies.

lim(x→a) p(x) = p(a) for a polynomial p

Worked examples

Find the limit of 9x² + 10 as x approaches -6.

9 × (-6)² + 10 = 334

334

Find the limit of 5x² + 17 as x approaches 8.

5 × (8)² + 17 = 337

337

Try it yourself

  1. Find the limit of 6x² + 19 as x approaches -5.

  2. Find the limit of 4x² + 12 as x approaches 1.

Check your understanding

Answers and marking notes
  1. 169

    6 × (-5)² + 19 = 169

  2. 16

    4 × (1)² + 12 = 16

Further reading and review references

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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.