**I. Evaluate the following limits:**

**Question 1.**

Solution:

**Question 2.Solution:**

**Question 3.Solution:**

**II. Evaluate the following limits:**

**Question 1.Solution:**

**Question 2.Solution:**

**Question 3.Solution:**

**Question 4.Solution:**

**III. Evaluate the following limits:**

**Question 1.Solution:**

**Question 2.Solution:**

**Question 3.Solution:**

**Question 4.Solution:**

**Question 5.Solution:**

**Question 6.Solution:**

**Question 7.Solution:**

**Question 8.Solution:**

**Question 9.Solution:**

**IV. In the following examples, given ∈ > 0, find a δ > 0 such that whenever, |x – a| < δ, we must have |f(x) – l| < ∈.**

**Question 1.**

**Question 2.**

**Question 3.**

Consider ∈ > 0 and |f(x) – l| < ∈

**Question 4.**

Since δ can be assumed as very small, let us choose δ < 1

∴ 0 < x < 2

∴ 2 < x + 2 < 4

∴ |x + 2| < 4

∴ |(x + 2)(x – 1)|< 4 |x – 1| …..(ii)

From (i) and (ii), we get