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Trigonometric Removable Discontinuity Limits worksheets

Resolve removable trigonometric discontinuities with standard sine limits and exact identities.

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Rewrite with h=x-a, apply standard trigonometric limits and simplify exactly.

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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 standard trigonometric limits to evaluate removable discontinuities.

Worked example

Find lim x→0 of sin(3x)/(2x).

Rewrite as (3/2)(sin(3x)/(3x)); the limit is 3/2.

Keep the original function and its excluded point visible while simplifying only for the limit.

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 SheetNameScoreTeacherDateTrigonometric Removable Discontinuity LimitsEvaluate each exact limit using standard trigonometric limits and identities.1.limx-2-2+12·sin-3·x+2x+2Exact limit:2.limx-12+sinx+1sin2·x+1Exact limit:3.limx0-1-1-cos-1·xx2Exact limit:4.limx11-cos-2·x-1-1sin2·x-12Exact limit:5.limx21+12·sin-1·x-23·x-2Exact limit:6.limx-12·-2-sin-2·x+12·sin-3·x+12·Exact limit:Angles are measured in radians. Keep every answer exact.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateTrigonometric Removable Discontinuity LimitsEvaluate each exact limit using standard trigonometric limits and identities.7.limx12·1+12·1-cos-1·x-12·x-12·2Exact limit:8.limx-21+12·cos-2·x+2-1sin3·x+22Exact limit:Angles are measured in radians. Keep every answer exact.math-sheet.comPage 2 of 2

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