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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$

$\frac{1}{4}$
$\frac{1}{2}$
2
4

hint Hint:

To find the limit of the equation we will first rationalise the equation then we will put the value of x when putting the value will not make the equation invalid.

The correct answer is: $1 fourth$

$Lt subscript x not stretchy rightwards arrow 4 end subscript fraction numerator square root of x minus 2 over denominator x minus 4 end fraction$
$equals limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator open parentheses square root of x close parentheses squared minus 2 squared end fraction equals limit as x rightwards arrow 4 of fraction numerator open parentheses square root of x minus 2 close parentheses over denominator open parentheses square root of x minus 2 close parentheses open parentheses square root of x plus 2 close parentheses end fraction equals limit as x rightwards arrow 4 of fraction numerator 1 over denominator square root of x plus 2 end fraction equals fraction numerator 1 over denominator square root of 4 plus 2 end fraction equals fraction numerator 1 over denominator 2 plus 2 end fraction equals 1 fourth$

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