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Chapter 7 Limits Ex 7.1

Chapter 7 Limits Ex 7.1

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