Lt_(x rarr0)(x)/(sqrt(x+4)-2)= -Turito

Maths-

General

Easy

Question

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction equals$

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

Hint:

In the question we will use L hospital theorem, $fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction$ .

The correct answer is: 4

$L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator x over denominator square root of x plus 4 end root minus 2 end fraction u sin g space L h o s p i t a l space t h e o r e m comma space equals L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator begin display style fraction numerator d blank over denominator d x end fraction end style x over denominator begin display style fraction numerator d blank over denominator d x end fraction end style square root of x plus 4 end root minus 2 end fraction equals L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator 2 square root of x plus 4 end root end fraction end style end fraction equals L t subscript x not stretchy rightwards arrow 0 end subscript 2 square root of x plus 4 end root equals 2 square root of 0 plus 4 end root equals 2 cross times 2 equals 4$

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Question

4

Hint:

Answer

The correct answer is: 4

Solution

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

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