University:
North Central College
Course:
MATH 140 | Precalculus
Academic year:

2019
Views:

144

Pages:

2
Author:

5CelestialChronicle

Pre-Calculus [Day 2] 12.2 Homework Name______________________ Finding Limits Algebraically & Graphically Evaluate the limit. 1. lim𝑥→ 3 (𝑥 3 + 2)(𝑥 2 − 5𝑥) 4. lim𝑥→ − 4 7. lim𝑥→ 2 𝑥 2 + 5𝑥 + 4 𝑥 2 + 3𝑥 − 4 𝑥 4 − 16 𝑥−2 𝑥 4 + 𝑥2 −6 2 2. lim𝑥→ 1 (𝑥 4 + 2𝑥 + 3) 3. lim𝑥→ − 2 √𝑥 4 + 3𝑥 + 6 5. lim𝑥→ 1 𝑥3 − 1 𝑥2 − 1 6. limℎ→ 0 8. limℎ→ 0 (3 + ℎ)− 1 − 3− 1 ℎ 9. lim𝑥→ − 4 |𝑥 + 4| √1 + ℎ − 1 ℎ 𝑥−1 𝑓(𝑥) = { 2 𝑥 − 4𝑥 + 6 10. Let if 𝑥 < 2 if 𝑥 ≥ 2 a. Find lim𝑥→ 2 − 𝑓(𝑥) b. lim𝑥→ 2 + 𝑓(𝑥) c. Does lim𝑥→ 2 𝑓(𝑥) exist? d. Sketch the graph of 𝑓(𝑥). 𝑥 if 𝑥 < 0 𝑓(𝑥) = {𝑥 2 if 0 < 𝑥 ≤ 2 8−𝑥 if 𝑥 > 2 11. Let a. Evaluate each limit, if it exists. (i) lim𝑥→ 0 + 𝑓(𝑥) (ii) lim𝑥→ 0 𝑓(𝑥) (iii) lim𝑥→ 1 𝑓(𝑥) (iv) lim𝑥→ 2 − 𝑓(𝑥) (v) lim𝑥→ 2 + 𝑓(𝑥) (vi) lim𝑥→ 2 𝑓(𝑥) b. Sketch the graph of 𝑓(𝑥). Answers: 1. −174 8. − 1 9 11aiii. 1 4 3 3. 4 4. 9. 0 10a. 1 10b. 2 11aiv. 4 11av. 2. 9 6 5 5. 3 2 10c. No 11avi. Does Not Exist 6. 1 2 11ai. 0 7. 32 11aii. 0