# Evaluate the following limits in Exercises 1 to 22: lim z→₁ (z¹/³ - 1)/(z¹/⁶ - 1)

**Solution:**

At z = 1, the value of the given function takes the form 0/0, which is an indeterminate form.

So we will evaluate the given limit differently.

Put z^{1/6} = x so that z → 1 as x → 1

Accordingly,

lim z→₁ (z^{1/3} - 1)/(z^{1/6} - 1) = lim ₓ→₁ (x^{2} - 1)/(x - 1)

= lim ₓ→₁ (x^{2} - 1^{2})/(x - 1)

= 2 × 1^{2 - 1} [∵ (x^{n} - a^{n})/(x - a) = na^{n - 1}]

= 2

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 10

## Evaluate the following limits in Exercises 1 to 22: lim z→₁ (z¹/³ - 1)/(z¹/⁶ - 1)

**Summary:**

The value of the limit lim z→₁ (z^{1/3} - 1)/(z^{1/6} - 1) is 2