Evaluate the given limit: limₓ→₂ (3x² - x - 10)/(x² - 4)

Solution:

At x = 2 , 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→₂ (3x² - x - 10)/(x² - 4)

= limₓ→₂ (x - 2)(3x + 5)/( x - 2)( x + 2)

= limₓ→₂ (3x + 5)/( x + 2)

= (3(2) + 5)/(2 + 2)

= 11/4

NCERT Solutions Class 11 Maths Chapter 13 Exercise 13.1 Question 7

Evaluate the given limit: limₓ→₂ (3x² - x - 10)/(x² - 4)

Summary:

The value of the limit limₓ→₂ (3x² - x - 10)/(x² - 4) is 11/4