MATH 11 – Differential Calculus
Problem Set No. 1
Limits and Differentiation Using Increment Method







Solve the following expressions.
Use yellow paper.
Write legibly.
Organize your solution.
Ink all your entries.
Box your final answer.
Avoid unnecessary major erasures.
3
Evaluate the following.
1.
21. lim (𝑥−2)
𝑥→2
lim (𝑥 + 3)1984
𝑥+2
𝑥→−4
22. lim (𝑥−3)
𝑥→3
1⁄
3
2.
lim(2𝑧 − 8)
3.
√3ℎ+1−1
)
ℎ
ℎ→0
24. lim (2𝑥 3 − 12𝑥 2 + 𝑥 − 7)
4.
√5ℎ+4−2
lim ( ℎ )
ℎ→0
25. lim (𝑥 2−7𝑥+3)
5.
6.
7.
8.
9.
23. lim (2𝑥 11 − 5𝑥 6 + 3𝑥 2 + 1)
𝑧→0
𝑥→∞
lim (
𝑥+3
lim (
𝑥→−3 𝑥 2 +4𝑥+3
lim (
𝑥→−∞
2𝑥+5
𝑥→+∞
)
26. lim (
𝑥→+∞
𝑢 4 −1
27. lim [
𝑚→0
𝑢 3 −8
28. lim [
𝑢→2
𝑥−1
𝑥→1 √𝑥+3−2
10. lim (
𝑚→0
)
𝑥+1
2−√𝑥 2 −5
𝑥+3
𝑥→−3
𝑚
𝑚
√𝑥 2+5−3
𝑥 2−2𝑥
] 𝑤ℎ𝑒𝑛 𝑓(𝑥) = 4𝑥 2 − 𝑥
] 𝑤ℎ𝑒𝑛 𝑓(𝑥) = √2𝑥
)
30. lim (√𝑥 2 + 𝑥 − 𝑥
)
𝑥→+∞
)
Solve for the first derivative using increment method.
4−𝑥
11. lim (
29. lim (
𝑥→2
√𝑥 2 +8−3
𝑥→−1
)
𝑓(𝑥+𝑚)−𝑓(𝑥)
lim (𝑢4−16)
lim (
7𝑥 3 +5
𝑓(𝑥+𝑚)−𝑓(𝑥)
)
𝑢→1 𝑢 3 −1
lim (
3𝑥 3 −4𝑥+2
𝑥→4 5−√𝑥 2 +9
)
Show your step-by-step solution.
1.
𝑓(𝑥 ) = 2𝑥 − 7
2.
𝑓(𝑥 ) = 𝐴𝑥 + 𝐵
13. lim ( 𝑥−1 )
3.
𝑓(𝑥 ) = 2𝑥 2 − 3𝑥 + 5
5𝑛 2 −4
4.
𝑓 (𝑥 ) = 𝑥 3
5.
𝑓(𝑥 ) = 7𝑥 5 − 3𝑥 4 + 6𝑥 2 + 3𝑥 + 4
12. lim (
𝑛→5
𝑛 2 −25
𝑛−5
)
𝑥 3 −1
𝑥→1
14. lim (
𝑛→0
15. lim (
𝑛+1
𝑥 2 −𝑥−12
𝑥−4
𝑥→4
16. lim (
𝑥 2 +3𝑥−4
𝑥 3 −5𝑥 2 +2𝑥−4
𝑥 2 −3𝑥34
𝑥→2
18. lim (
𝑥→0
)
𝑥 4 +3𝑥 3 −13𝑥 2 −27𝑥+36
𝑥→1
17. lim (
)
)
XXXXXX NOTHING FOLLOWS XXXXXX
)
√𝑥+3−√3
)
𝑥
1
4
19. lim (𝑥−2 − 𝑥 2−4)
𝑥→2
1
20. lim ((𝑥−3)2 )
𝑥→3
KACrystal. April 2023