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 (𝑥 3 + 2𝑥 2 − 3𝑥 − 4)
𝑥→−1
2. lim
𝑥→−3
𝑥 2 −5𝑥−24
𝑥+3
2. LIMITS AND CONTINUITY
1
3. lim 𝑥 2 cos 𝑥
𝑥→0
4. lim
𝑥 2 −1
𝑥→1 𝑥 3 −1
sin 5𝑥
5. lim sin 7𝑥
𝑥→0
2. LIMITS AND CONTINUITY
6. lim𝜋 tan 𝑥
𝑋→
2
7. lim
sin 2𝑥+sin 3𝑥
𝑥→0
𝑥
√𝑥−2
𝑥→4 𝑥−4
8. lim
2. LIMITS AND CONTINUITY
√𝑥−2
9. lim 𝑥2 −4
𝑥→2
10. lim
𝑥 2 +3𝑥+2
𝑥→−1 𝑥 2 +4𝑥+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
𝑥→∞
2. lim
𝑥→∞
𝑥 2 +5𝑥+6
𝑥+1
5𝑥 3 −𝑥 2 +10
𝑥 4 +𝑥+3
2. LIMITS AND CONTINUITY
3. lim
2𝑥 2 +1
𝑥→∞ 6+𝑥−3𝑥 2
4. lim
𝑥→∞
5. lim
3𝑥 4 +100𝑥 3 +4
8𝑥 4 +1
5𝑥+2
𝑥→∞ √4𝑥 2 −15
2. LIMITS AND CONTINUITY