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Calculus Limit Problems

1. The document provides examples of evaluating limits using algebraic manipulation. It gives 23 practice problems evaluating various limits as x approaches a number. It then provides 4 test questions asking to evaluate specific limits. The examples cover direct substitution, factoring, canceling, limits of trigonometric functions, and undefined/nonexistant limits.

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Azra Ozen
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2K views3 pages

Calculus Limit Problems

1. The document provides examples of evaluating limits using algebraic manipulation. It gives 23 practice problems evaluating various limits as x approaches a number. It then provides 4 test questions asking to evaluate specific limits. The examples cover direct substitution, factoring, canceling, limits of trigonometric functions, and undefined/nonexistant limits.

Uploaded by

Azra Ozen
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Calculus 1.

6 Algebraic Manipulation (Limits) Notes


Write your questions
and thoughts here!
Direct Substitution Factor and Cancel
1. lim (𝑥 + 2𝑥 − 4) 2. lim 6 3. lim 4. lim
→ →
→ →

Limit Does Not Exist


5. lim
→

Special Trig Limits:


sin 𝑥 𝑥
lim =1 lim =1
→ 𝑥 or → sin 𝑥

1 − cos 𝑥 cos 𝑥 − 1
lim =0 or lim =0
→ 𝑥 → 𝑥

6. lim 7. lim 8. lim


→ → → ( )
1.6 Algebraic Manipulation of Limits
Calculus
Practice
Evaluate each limit.
1. lim (𝑥 − 𝑥 ) 2. lim (𝑥 + 1) 3. lim 4. lim
→ →
→ →

5. lim 6. lim
( ) 7. lim (3𝑥 − 𝑥 + 1) 8. lim (2𝑥 + 5𝑥 − 6)
→ → → →

9. lim 10. lim 11. lim 12. lim


→ → → →

13. lim 14 14. lim 15. lim 16. lim


→
→ → →
17. lim 18. lim 19. lim cos 𝑥 20. lim sin(4𝑥)
→ →
→ →

21. lim 22. lim 23. lim


→ → →

1.6 Algebraic Manipulation of Limits Test Prep


24. Evaluate lim is
→

(A) 0 (B) (C) 𝑒 (D) 3 (E) The limit does not exist.

25. lim 4 is
→

(A) 2 (B) (C) ∞ (D) 0 (E) undefined

26. lim =
→

(A) −∞ (B) 𝑎 (C) 0 (D) ∞ (E) The limit does not exist.

27. lim =
→

(A) 0 (B) (C) 3 (D) 4 (E) Does not exist

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