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Limits: Factoring & Limits at Infinity — Easy Worksheet 1
Grade 12 · MathSheets Name: ____________________ Date: __________
Evaluate each limit. Give fractions in simplest form.
How to solve
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Example
Find the limit: lim(x→-8) of x² - 64x + 8
Answer: -16
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→8) of x² - 64x - 8
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→7) of x² - 49x - 7
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→-9) of x² - 81x + 9
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→5) of x² - 25x - 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→4) of x² - 16x - 4
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→3) of x² - 9x - 3
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→-5) of x² - 25x + 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Limits: Factoring & Limits at Infinity
If substituting gives 00, factor and cancel the common factor (or multiply by the conjugate for square roots), then substitute. As x → ∞, compare degrees: a bigger denominator degree gives 0, equal degrees give the ratio of the leading coefficients.
Try a similar one
Find the limit: lim(x→9) of x² - 81x - 9
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Limits: Factoring & Limits at Infinity — Easy Worksheet 1
Evaluate each limit. Give fractions in simplest form.