Assignment 2A – Limits of a Function
Evaluate each of the following:
1. lim (𝑥 2 − 4𝑥 + 3)
𝑥→2
2. lim
4𝑥+2
𝑥→3 𝑥+4
3. lim𝜋 (𝑡𝑎𝑛𝑥 + 𝑠𝑖𝑛𝑥)
𝑥→
4
4. lim𝜋
𝑥→
𝑠𝑖𝑛2𝑥
𝑠𝑖𝑛𝑥
3
3
5. lim (2𝑛 + √𝑛 − 4)
𝑛→8
6. lim (4𝑥 − 3)(𝑥 2 + 5)
𝑥→2
√3𝑛
𝑛→3 𝑛√𝑛+1
7. lim
8. lim
𝑥→0
3𝑥+2
𝑥 2 −2𝑥+4
Assignment 2B – Indeterminate Forms
Evaluate each of the following:
1. lim
𝑥 3 −64
𝑥→4 𝑥 2 −16
𝑥 3 −13𝑥+12
2. lim 𝑥 3 −14𝑥+15
𝑥→3
3. lim
𝑥→0
4. lim
(𝑥+3)2 −9
2𝑥
𝑥−1
𝑥→1 √𝑥+3−2
1
−
1
5. lim 𝑥𝑥−44
𝑥→4
6. lim
𝑥−3
𝑥→3 √𝑥−2 − √4−𝑥
7. lim
𝑥→3
8. lim
√𝑥 2 −9
𝑥−3
𝑠𝑖𝑛3 𝑥
𝑥→0 𝑠𝑖𝑛𝑥−𝑡𝑎𝑛𝑥
9. lim
𝑥→0
𝑠𝑖𝑛 𝑥 𝑠𝑖𝑛 2𝑥
1−𝑐𝑜𝑠 𝑥