Evaluate the following limits in Exercises 1 to 22: limₓ→₃ (x⁴ - 81)/(2x - 5x - 3)

Solution:

At x = 3, the value of the given rational function takes the form 0/0, which is an indeterminate form.

So we will evaluate the given limit differently.

limₓ→₃ (x⁴ - 81)/(2x - 5x - 3)

= limₓ→₃ (x - 3)(x + 3)(x² + 9)/(x - 3)(2x + 1)

= limₓ→₃ (x + 3)(x² + 9)/(2x + 1)

= (3 + 3)(3² + 9)/(2 (3) + 1)

= (6 × 18)/(6 + 1)

= 108/7

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 8

Evaluate the following limits in Exercises 1 to 22: limₓ→₃ (x⁴ - 81)/(2x - 5x - 3)

Summary:

The value of the limit limₓ→₃ (x⁴ - 81)/(2x - 5x - 3) is 108/7