Limits Worksheets
Free printable limits worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from direct substitution: lim of ax + b at the easy level through to indeterminate 0/0 resolved by rationalization at the advanced level.
LK20.R1LK20.S1
Difficulty Levels
Beginner
- Concepts
- Direct substitution: lim of ax + b
- Number Range
- a: −3 to 5, b: −6 to 6, c: 1–6
- Steps
- 2 steps
- Example
- lim(x→3) (2x + 1)
Easy
- Concepts
- Factor and cancel 0/0 form: (x²−r²)/(x−r)
- Number Range
- r: −3 to 5
- Steps
- 4 steps
- Example
- lim(x→2) (x²−4)/(x−2)
Medium
- Concepts
- Limits at infinity of rational functions
- Number Range
- coefficients: 1–5, degree comparison
- Steps
- 3 steps
- Example
- lim(x→∞) (3x²+1)/(2x²−4)
Hard
- Concepts
- Indeterminate 0/0 resolved by rationalization
- Number Range
- a: 1–5
- Steps
- 5 steps
- Example
- lim(x→0) (√(x+4)−2)/x
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