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Grade 12 · Math

Evaluate a polynomial limit

Use continuity to evaluate a polynomial limit by substitution.

8 authored questions + worked example

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Worked example

Find the limit of 2x2 + (3)x + (1) as x approaches 2.

Answer & why

Answer: 15

Polynomials are continuous. Substitute x=2: 2(2)2 + (3)(2) + (1) = 15.

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All questions

All 8 authored questions for this skill.

Question 1

Find the limit of 1x2 + (-4)x + (6) as x approaches 5.

  1. 11
  2. 12
  3. 13
  4. 10
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 11

Polynomials are continuous. Substitute x=5: 1(5)2 + (-4)(5) + (6) = 11.

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Question 2

Find the limit of 2x2 + (5)x + (3) as x approaches -3.

  1. 6
  2. 7
  3. 5
  4. 8
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 6

Polynomials are continuous. Substitute x=-3: 2(-3)2 + (5)(-3) + (3) = 6.

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Question 3

Find the limit of 2x2 + (3)x + (1) as x approaches 2.

  1. 17
  2. 14
  3. 16
  4. 15
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 15

Polynomials are continuous. Substitute x=2: 2(2)2 + (3)(2) + (1) = 15.

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Question 4

Find the limit of 3x2 + (-2)x + (4) as x approaches 1.

  1. 5
  2. 6
  3. 4
  4. 7
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 5

Polynomials are continuous. Substitute x=1: 3(1)2 + (-2)(1) + (4) = 5.

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Question 5

Find the limit of 1x2 + (5)x + (-3) as x approaches 3.

  1. 21
  2. 23
  3. 22
  4. 20
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 21

Polynomials are continuous. Substitute x=3: 1(3)2 + (5)(3) + (-3) = 21.

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Question 6

Find the limit of 4x2 + (1)x + (2) as x approaches -1.

  1. 5
  2. 7
  3. 4
  4. 6
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 5

Polynomials are continuous. Substitute x=-1: 4(-1)2 + (1)(-1) + (2) = 5.

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Question 7

Find the limit of 2x2 + (-3)x + (5) as x approaches 4.

  1. 27
  2. 24
  3. 25
  4. 26
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 25

Polynomials are continuous. Substitute x=4: 2(4)2 + (-3)(4) + (5) = 25.

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Question 8

Find the limit of 3x2 + (2)x + (-1) as x approaches -2.

  1. 8
  2. 6
  3. 9
  4. 7
A hint

For a polynomial, evaluate at the approached value.

Answer & why

Answer: 7

Polynomials are continuous. Substitute x=-2: 3(-2)2 + (2)(-2) + (-1) = 7.

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