# Evaluate: limx→2x2-43x-2-x+2 - Mathematics

Sum

Evaluate: lim_(x -> 2) (x^2 - 4)/(sqrt(3x - 2) - sqrt(x + 2))

#### Solution

Given that lim_(x -> 2) (x^2 - 4)/(sqrt(3x - 2) - sqrt(x + 2))

Rationalizing the denominator, we get

= lim_(x -> 2) ((x - 2)(x + 2) [sqrt(3x - 2) + sqrt(x + 2)])/([sqrt(3x - 2) - sqrt(x + 2)][sqrt(3x - 2) + sqrt(x + 2)])

= lim_(x -> 2) ((x - 2)(x + 2)[sqrt(3x - 2) + sqrt(x + 2)])/(3x - 2 - x - 2)

= lim_(x -> 2) ((x - 2)(x + 2)[sqrt((3x - 2)) + sqrt(x + 2)])/(2x - 4)

= lim_(x -> 2) ((x - 2)(x + 2) [sqrt((3x - 2)) + sqrt(x + 2)])/(2(x - 2))

= lim_(x -> 2) ((x + 2)[sqrt(3x - 2) + sqrt(x + 2)])/2

Taking limits, we have

= ((2 + 2)[sqrt(6 - 2) + sqrt(2 + 2)])/2

= (4[2 + 2])/2

= (4 xx 4)/2

= 8

Concept: Concept of Limits - Limits of Polynomials and Rational Functions
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 13 Limits and Derivatives
Exercise | Q 8 | Page 240