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Maths-

General

Easy

Question

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

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

hint Hint:

Factorize the denominator and solve the limits.

The correct answer is: $1 fourth$

$limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator x minus 4 end fraction equals limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator open parentheses square root of x close parentheses squared minus open parentheses 2 close parentheses squared end fraction equals limit as x rightwards arrow 4 of fraction numerator square root of x minus 2 over denominator open parentheses square root of x minus 2 close parentheses open parentheses square root of x plus 2 close parentheses end fraction equals limit as x rightwards arrow 4 of fraction numerator 1 over denominator open parentheses square root of x plus 2 close parentheses end fraction equals fraction numerator 1 over denominator open parentheses square root of 4 plus 2 close parentheses end fraction equals fraction numerator 1 over denominator open parentheses 2 plus 2 close parentheses end fraction equals 1 fourth$

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If $text end text f colon left square bracket negative 2 comma 2 right square bracket rightwards arrow R text is end text$ defined by $f left parenthesis x right parenthesis equals open curly brackets table row cell fraction numerator square root of 1 plus c x end root minus square root of 1 minus c x end root over denominator x end fraction comma text end text text f end text text o end text text r end text text end text minus 2 less or equal than x less than 0 end cell row cell fraction numerator x plus 3 over denominator x plus 1 end fraction comma text end text text f end text text o end text text r end text text end text 0 less or equal than x less or equal than 2 end cell end table close$ is continuous on [-2,2] then c =

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