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Calculus practice

Simple Limit Evaluation worksheets

Evaluate exact finite-point limits for polynomial, rational, exponential and trigonometric functions.

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Evaluate every limit exactly by direct substitution. State any original-domain restriction.

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Keep the original function visible

These worksheets preserve exact values and original-domain restrictions while separating direct continuity from removable-discontinuity reasoning.

Learning objective

What this activity builds

Use continuity and exact substitution to evaluate finite limits.

Worked example

Find lim x→2 of (x²+1).

Direct substitution gives 2²+1=5.

Check that the original expression is defined at the point, then substitute exactly.

Teaching notes

Make the practice count

  • Keep fractions, radicals, pi and powers of e exact.
  • Distinguish the original function from its continuous extension.
  • Use radians for every trigonometric expression.

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Choose 6, 8, or 10 exact finite-limit problems. Presentation choices do not change the generated mathematics.

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Math SheetNameScoreTeacherDateSimple Limit EvaluationEvaluate each finite-point limit exactly by direct substitution.1.limx16·1-sinxExact limit:2.limx3-6·x+5Exact limit:3.limx-2-2+2·ex-2Exact limit:4.limx34·x-5-4·x-5Exact limit:5.limx14·2·cosxExact limit:6.limx-1-6·x2+6·x+1Exact limit:Angles are measured in radians. Keep every answer exact.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateSimple Limit EvaluationEvaluate each finite-point limit exactly by direct substitution.7.limx02+2xExact limit:8.limx-32-3·x2+x-62·x-2Exact limit:9.limx13·-1-tanxExact limit:10.limx-32-2·x3+2·x2-6·x+5Exact limit:Angles are measured in radians. Keep every answer exact.math-sheet.comPage 2 of 2

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