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 = −1

Find the limit L = limx→−1 (x2 − 5x − 6)/(x + 1).

f(x) = (x2 − 5x − 6)/(x + 1)x → −1
L =
2.Easy
xy16x = 16

Find the limit L = limx→16 (√x − 4)/(x − 16).

f(x) = (√x − 4)/(x − 16)x → 16
L =
3.Medium
xyy = L

Find the limit L = limx→∞ (1 − 1/x)x. Give a decimal value.

f(x) = (1 − 1/x)xx → ∞
L =
4.Medium
xyy = L

Find the limit L = limx→∞ (1 − 1/x)3x. Give a decimal value.

f(x) = (1 − 1/x)3xx → ∞
L =
5.Hard
xyx = 0

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

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

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

f(x) = (e2x − 1 − 2x)/x²x → 0
L =

Answer key

  1. 1. L = −7
  2. 2. L = 0.125
  3. 3. L = 0.3679
  4. 4. L = 0.04979
  5. 5. L = 0.5
  6. 6. L = 2

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