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 = 2

Find the limit L = limx→2 (x2 + x − 6)/(x − 2).

f(x) = (x2 + x − 6)/(x − 2)x → 2
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 − 6x) − 3x).

f(x) = √(9x2 − 6x) − 3xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (√(4x2 − 9x) − 2x).

f(x) = √(4x2 − 9x) − 2xx → ∞
L =
5.Hard
xyx = 0

Find the limit L = limx→0 ln(1 + 3x)/sin(4x), with x in radians.

f(x) = ln(1 + 3x)/sin(4x)x → 0
L =
6.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 =

Answer key

  1. 1. L = 27
  2. 2. L = 5
  3. 3. L = −1
  4. 4. L = −2.25
  5. 5. L = 0.75
  6. 6. L = 8

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