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→−2 (x⁴ − 16)/(x + 2).

f(x) = (x⁴ − 16)/(x + 2)x → −2

L =

2.Easy

Find the limit L = lim_x→2 (x³ − 8)/(x − 2).

f(x) = (x³ − 8)/(x − 2)x → 2

L =

3.Medium

Find the limit L = lim_x→∞ (6x³ + 3x + 7)/(x³ + 2x + 9).

f(x) = (6x³ + 3x + 7)/(x³ + 2x + 9)x → ∞

L =

4.Medium

Find the limit L = lim_x→∞ (−4x² + x + 4)/(x² + 2x + 6).

f(x) = (−4x² + x + 4)/(x² + 2x + 6)x → ∞

L =

5.Hard

Find the limit L = lim_x→0 (1 − cos 5x)/(2x²), with x in radians.

f(x) = (1 − cos 5x)/(2x²)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 = −32
2. L = 12
3. L = 6
4. L = −4
5. L = 6.25
6. L = 1.125

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