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CHAPTER 2 - Exercises

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Name: _______________________________
Id Number:__________
Section: __________
Score: _____________
EXERCISE 2.1
LIMITS OF A FUNCTION
Objective
After completing this chapter, the students should be able to:
1. Solve the limit of functions using the knowledge gained in algebra.
2. Realize the relevance of limits as a foundation of calculus
3. Familiarize themselves to the use of special limiting values in evaluating limits.
Direction. Evaluate the limit of the following functions.
1. lim (π‘₯ 3 + 2π‘₯ 2 − 3π‘₯ − 4)
π‘₯→−1
2. lim
π‘₯→−3
π‘₯ 2 −5π‘₯−24
π‘₯+3
2. LIMITS AND CONTINUITY
1
3. lim π‘₯ 2 cos π‘₯
π‘₯→0
4. lim
π‘₯ 2 −1
π‘₯→1 π‘₯ 3 −1
sin 5π‘₯
5. lim sin 7π‘₯
π‘₯→0
2. LIMITS AND CONTINUITY
6. limπœ‹ tan π‘₯
𝑋→
2
7. lim
sin 2π‘₯+sin 3π‘₯
π‘₯→0
π‘₯
√π‘₯−2
π‘₯→4 π‘₯−4
8. lim
2. LIMITS AND CONTINUITY
√π‘₯−2
9. lim π‘₯2 −4
π‘₯→2
10. lim
π‘₯ 2 +3π‘₯+2
π‘₯→−1 π‘₯ 2 +4π‘₯+3
2. LIMITS AND CONTINUITY
Name: _______________________________
Id Number:__________
Section: __________
Score: _____________
EXERCISE 2.2
LIMITS OF A FUNCTION
Objective
After completing this chapter, the students should be able to:
1. Solve the limit of functions using the knowledge gained in algebra.
2. Realize the relevance of limits as a foundation of calculus
3. Familiarize themselves to the use of special limiting values in evaluating limits.
Direction. Evaluate the limit of the following functions.
1. lim
π‘₯→∞
2. lim
π‘₯→∞
π‘₯ 2 +5π‘₯+6
π‘₯+1
5π‘₯ 3 −π‘₯ 2 +10
π‘₯ 4 +π‘₯+3
2. LIMITS AND CONTINUITY
3. lim
2π‘₯ 2 +1
π‘₯→∞ 6+π‘₯−3π‘₯ 2
4. lim
π‘₯→∞
5. lim
3π‘₯ 4 +100π‘₯ 3 +4
8π‘₯ 4 +1
5π‘₯+2
π‘₯→∞ √4π‘₯ 2 −15
2. LIMITS AND CONTINUITY
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