Limits at Infinity Worksheet 8

Evaluate limits with the approach direction stated and distinguish limits from function values.

hard: Use another set to practice explaining and checking your answers.

23 problems · 20-25 minutes · Skills: limits, asymptotes, calculus

About This Worksheet

This hard-level worksheet contains 23 problems designed for 12th Grade students practicing limits at infinity. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

Evaluate limits with the approach direction stated and distinguish limits from function values.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Find lim as x → +∞ of (4x² + 4)/(7x² + 1).

Solution Steps:

Divide the numerator and denominator by x².
Terms with 1/x² vanish, leaving the ratio of leading coefficients.

Answer: 4/7

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

Find lim as x → +∞ of (2x² + 4)/(1x² + 1).

Find lim as x → +∞ of (8x² + 6)/(7x² + 1).

Find lim as x → +∞ of (7x² + 6)/(9x² + 1).

Find lim as x → +∞ of (1x² + 3)/(4x² + 1).

Find lim as x → +∞ of (4x² + 8)/(5x² + 1).

Find lim as x → +∞ of (2x² + 5)/(9x² + 1).

Find lim as x → +∞ of (7x² + 2)/(7x² + 1).

Find lim as x → +∞ of (1x² + 8)/(7x² + 1).

Find lim as x → +∞ of (8x² + 8)/(8x² + 1).

Find lim as x → +∞ of (6x² + 2)/(9x² + 1).

Find lim as x → +∞ of (1x² + 2)/(3x² + 1).

Find lim as x → +∞ of (2x² + 2)/(2x² + 1).

Find lim as x → +∞ of (4x² + 3)/(7x² + 1).

Find lim as x → +∞ of (6x² + 3)/(1x² + 1).

Find lim as x → +∞ of (1x² + 9)/(3x² + 1).

Find lim as x → +∞ of (2x² + 4)/(3x² + 1).

Find lim as x → +∞ of (6x² + 7)/(4x² + 1).

Find lim as x → +∞ of (1x² + 7)/(3x² + 1).

Find lim as x → +∞ of (4x² + 3)/(9x² + 1).

Find lim as x → +∞ of (8x² + 7)/(5x² + 1).

Find lim as x → +∞ of (3x² + 3)/(3x² + 1).

Find lim as x → +∞ of (6x² + 6)/(1x² + 1).

Find lim as x → +∞ of (1x² + 5)/(6x² + 1).

Answer Key

1. 22. 8/73. 7/94. 1/45. 4/56. 2/97. 18. 1/79. 110. 2/311. 1/312. 113. 4/714. 615. 1/316. 2/317. 3/218. 1/319. 4/920. 8/521. 122. 623. 1/6

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Frequently Asked Questions

How do I download this limits at infinity - worksheet 8 worksheet?

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How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this limits & continuity worksheet cover?

This worksheet focuses on limits, asymptotes, calculus. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 23 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.