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Maths-

General

Easy

Question

If $f left parenthesis x right parenthesis equals negative square root of 25 minus x squared end root comma text then end text L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals$

$\frac{1}{24}$
$\frac{1}{5}$
$- \sqrt{24}$
$\frac{1}{\sqrt{24}}$

hint Hint:

In the question first we will use the L hospital theorem, then after putting the value of f(x) we will get the answer.

The correct answer is: $fraction numerator 1 over denominator square root of 24 end fraction$

Given, $f left parenthesis x right parenthesis equals negative square root of 25 minus x squared end root$
$L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction u sin g space L space h o s p i t a l space t h e o r e m comma equals L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator begin display style fraction numerator d blank over denominator d x end fraction end style f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator begin display style fraction numerator d blank over denominator d x end fraction end style x minus 1 end fraction equals L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f apostrophe left parenthesis x right parenthesis over denominator 1 end fraction equals L t subscript x not stretchy rightwards arrow 1 space end subscript f apostrophe left parenthesis x right parenthesis equals L t subscript x not stretchy rightwards arrow 1 space end subscript fraction numerator d left parenthesis negative square root of 25 minus x squared end root right parenthesis over denominator d x end fraction equals L t subscript x not stretchy rightwards arrow 1 space end subscript fraction numerator negative 1 cross times negative 2 over denominator 2 square root of 25 minus x squared end root end fraction equals L t subscript x not stretchy rightwards arrow 1 space end subscript fraction numerator 1 over denominator square root of 25 minus x squared end root end fraction equals fraction numerator 1 over denominator square root of 25 minus 1 end root end fraction equals fraction numerator 1 over denominator square root of 24 end fraction$

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