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.

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1.Easy

Find the limit L = lim_x→0 (x² + 4x)/(x).

f(x) = (x² + 4x)/(x)x → 0

L =

2.Easy

Find the limit L = lim_x→36 (√x − 6)/(x − 36).

f(x) = (√x − 6)/(x − 36)x → 36

L =

3.Medium

Find the limit L = lim_x→∞ (−5x² − 6x − 5)/(5x² + 6x + 2).

f(x) = (−5x² − 6x − 5)/(5x² + 6x + 2)x → ∞

L =

4.Medium

Find the limit L = lim_x→∞ (−4x² − 5x − 7)/(2x² + 3x + 9).

f(x) = (−4x² − 5x − 7)/(2x² + 3x + 9)x → ∞

L =

5.Hard

Find the limit L = lim_x→0 (1 − cos 2x)/(x²), with x in radians.

f(x) = (1 − cos 2x)/(x²)x → 0

L =

6.Hard

Find the limit L = lim_x→0 (1 − cos 3x)/(4x²), with x in radians.

f(x) = (1 − cos 3x)/(4x²)x → 0

L =

Answer key

1. L = 4
2. L = 0.08333
3. L = −1
4. L = −2
5. L = 2
6. L = 1.125

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