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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow 3 end subscript fraction numerator x minus 3 over denominator square root of open vertical bar x squared minus 9 close vertical bar end root end fraction$

1
3
0
9

hint Hint:

In this question, $space open vertical bar x squared minus 9 close vertical bar equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell x squared minus 9 end cell cell comma space i f space x greater or equal than 3 end cell row cell x squared minus 9 end cell cell comma space i f space x less than 3 end cell end table close$ we will consider $x squared minus 9$ as x=3. Then we will evaluate and later put the value of x.

The correct answer is: 0

$space space space limit as x rightwards arrow 3 of space fraction numerator x minus 3 over denominator square root of open vertical bar x squared minus 9 close vertical bar end root end fraction w h e r e comma space open vertical bar x squared minus 9 close vertical bar equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell x squared minus 9 end cell cell comma space i f space x greater or equal than 3 end cell row cell x squared minus 9 end cell cell comma space i f space x less than 3 end cell end table close equals limit as x rightwards arrow 3 of space fraction numerator x minus 3 over denominator square root of x squared minus 9 end root end fraction equals limit as x rightwards arrow 3 of space fraction numerator square root of left parenthesis x minus 3 right parenthesis left parenthesis x minus 3 right parenthesis end root over denominator square root of open parentheses x plus 3 right parenthesis left parenthesis x minus 3 close parentheses end root end fraction equals limit as x rightwards arrow 3 of space fraction numerator square root of x minus 3 end root over denominator square root of x plus 3 end root end fraction equals fraction numerator square root of 3 minus 3 end root over denominator square root of 3 plus 3 end root end fraction equals 0 over 6 equals 0$

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