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
xy9x = 9

Find the limit L = limx→9 (√x − 3)/(x − 9).

f(x) = (√x − 3)/(x − 9)x → 9
L =
2.Easy
xy4x = 4

Find the limit L = limx→4 (√x − 2)/(x − 4).

f(x) = (√x − 2)/(x − 4)x → 4
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (√(9x2 − 4x) − 3x).

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

Find the limit L = limx→∞ (√(4x2 + 5x) − 2x).

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

Find the limit L = limx→0 (e2x − 1 − 2x)/x².

f(x) = (e2x − 1 − 2x)/x²x → 0
L =
6.Hard
xyx = 0

Find the limit L = limx→0 (1 − cos 5x)/(3x²), with x in radians.

f(x) = (1 − cos 5x)/(3x²)x → 0
L =

Answer key

  1. 1. L = 0.1667
  2. 2. L = 0.25
  3. 3. L = −0.6667
  4. 4. L = 1.25
  5. 5. L = 2
  6. 6. L = 4.167

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