Grade 12 · Math · Calculus

12th grade Limits with absolute value and trig worksheet

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Limits with absolute value and trig

Grade 12 Math Worksheet - Building Confidence

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Ari works with the sine limit near zero. What is the limit of sin(3x)/(2x) as x → 0?
Bo works with the sine limit near zero. What is the limit of sin(5x)/(4x) as x → 0?
Esme works with the sine limit near zero. What is the limit of sin(2x)/(3x) as x → 0?
Kira studies f(x) = 3|x − 2|/(x − 2) + 1. What is the limit of f(x) as x → 2⁻?
Luz studies f(x) = 4|x + 1|/(x + 1) + 2. What is the limit of f(x) as x → -1⁻?
Milo studies f(x) = 2|x − 5|/(x − 5) + 8. What is the limit of f(x) as x → 5⁻?
Pia works with the tangent limit near zero. What is the limit of tan(4x)/(3x) as x → 0?
Ren works with the tangent limit near zero. What is the limit of tan(7x)/(2x) as x → 0?
Tala works with the tangent limit near zero. What is the limit of tan(3x)/(8x) as x → 0?
Zee works with the tangent limit near zero. What is the limit of tan(9x)/(4x) as x → 0?

Limits with absolute value and trig. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

sin u/u → 1: As u shrinks to 0, sin u and u become almost equal.

squeeze theorem: If f is trapped between two functions that meet, f meets them too.

Used sin u/u → 1 without matching the inside. sin(3x)/x needs a 3x on the bottom, so it heads to 3.

Flipped the two numbers. The number inside the top's function goes on top.

Treated |x − 2| as x − 2 on the left, where x − 2 is negative. Left of 2, |x − 2| = −(x − 2).

What is the most common mistake with limits with absolute value and trig?

Used sin u/u → 1 without matching the inside. sin(3x)/x needs a 3x on the bottom, so it heads to 3.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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