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Introduction to Limits — Easy Worksheet 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Evaluate each limit. These functions are continuous everywhere, so the limit equals the function value at that point (direct substitution).
How to solve
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Example
Find the limit: lim(x→1) of 6x
Answer: 6
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -4. Substitute x = -4: 4(-4) − 6 = -16 − 6 = -22. The limit is -22.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -4. Substitute x = -4: 4(-4) − 6 = -16 − 6 = -22. The limit is -22.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→2) of 3x - 3
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -3. Substitute x = -3: 6(-3) + 7 = -18 + 7 = -11. The limit is -11.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -3. Substitute x = -3: 6(-3) + 7 = -18 + 7 = -11. The limit is -11.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→4) of 2x - 1
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -2. Substitute x = -2: -2 + 8 = 6. The limit is 6.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -2. Substitute x = -2: -2 + 8 = 6. The limit is 6.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→-2) of 6x - 4
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -1. Substitute x = -1: 5(-1) − 1 = -5 − 1 = -6. The limit is -6.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = -1. Substitute x = -1: 5(-1) − 1 = -5 − 1 = -6. The limit is -6.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→0) of 3x + 7
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 1. Substitute x = 1: 2(1) − 3 = 2 − 3 = -1. The limit is -1.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 1. Substitute x = 1: 2(1) − 3 = 2 − 3 = -1. The limit is -1.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→0) of 4x - 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 2. Substitute x = 2: 2(2) + 6 = 4 + 6 = 10. The limit is 10.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 2. Substitute x = 2: 2(2) + 6 = 4 + 6 = 10. The limit is 10.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→1) of 4x - 6
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 3. Substitute x = 3: 5(3) − 1 = 15 − 1 = 14. The limit is 14.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 3. Substitute x = 3: 5(3) − 1 = 15 − 1 = 14. The limit is 14.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→-5) of 6x + 3
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 2. Substitute x = 2: 5(2) + 4 = 10 + 4 = 14. The limit is 14.
✓ Correct!
Not quite. The answer is
💡 A polynomial is continuous, so the limit is just its value at x = 2. Substitute x = 2: 5(2) + 4 = 10 + 4 = 14. The limit is 14.
💡 How to solve: Introduction to Limits
For a polynomial, the limit as x approaches a equals the function value at a. Use direct substitution: replace x with a and simplify.
Try a similar one
Find the limit: lim(x→4) of 4x + 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Introduction to Limits — Easy Worksheet 2
Evaluate each limit. These functions are continuous everywhere, so the limit equals the function value at that point (direct substitution).