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→−1 (x⁴ − 1)/(x + 1).

f(x) = (x⁴ − 1)/(x + 1)x → −1

L =

2.Easy

Find the limit L = lim_x→−3 (x³ + 27)/(x + 3).

f(x) = (x³ + 27)/(x + 3)x → −3

L =

3.Medium

Find the limit L = lim_x→∞ (6x³ + 2x + 3)/(4x³ + 4x + 7).

f(x) = (6x³ + 2x + 3)/(4x³ + 4x + 7)x → ∞

L =

4.Medium

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

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

L =

5.Hard

Find the limit L = lim_x→0 (e^1.5x − 1 − 1.5x)/x².

f(x) = (e^1.5x − 1 − 1.5x)/x²x → 0

L =

6.Hard

Find the limit L = lim_x→0 (1 − cos 3x)/(2x²), with x in radians.

f(x) = (1 − cos 3x)/(2x²)x → 0

L =

Answer key

1. L = −4
2. L = 27
3. L = 1.5
4. L = 0.3333
5. L = 1.125
6. L = 2.25

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