Limits worksheet with answers

Free printable Limits worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xyx = −3

Find the limit L = limx→−3 (x3 + 27)/(x + 3).

f(x) = (x3 + 27)/(x + 3)x → −3
L =
2.Easy
xyx = −4

Find the limit L = limx→−4 (x2 + 7x + 12)/(x + 4).

f(x) = (x2 + 7x + 12)/(x + 4)x → −4
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(x2 − 3x) − x).

f(x) = √(x2 − 3x) − xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (2x3 − 6x − 9)/(3x3 + 4x + 6).

f(x) = (2x3 − 6x − 9)/(3x3 + 4x + 6)x → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 4x)/(x²), with x in radians.

f(x) = (1 − cos 4x)/(x²)x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 5x)/(4x²), with x in radians.

f(x) = (1 − cos 5x)/(4x²)x → 0
L =

Answer key

  1. 1. L = 27
  2. 2. L = −1
  3. 3. L = −1.5
  4. 4. L = 0.6667
  5. 5. L = 8
  6. 6. L = 3.125

Full step-by-step solutions: practise this topic on examproblems.com.