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Maths-

General

Easy

Question

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 2 plus cos squared space x over denominator x plus 2007 end fraction$

1
0
-1
$\infty$

hint Hint:

In the question we will use L Hospital theorem first $open parentheses i. e. comma space fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction equals fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction close parentheses$ and then put the value of x.

The correct answer is: 0

$Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 2 plus cos squared space x over denominator x plus 2007 end fraction U sin g space L space H o s p t a l space t h e o r e m comma space equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator begin display style fraction numerator d blank over denominator d x end fraction end style 2 plus cos squared space x over denominator begin display style fraction numerator d blank over denominator d x end fraction end style x plus 2007 end fraction equals Lt subscript x not stretchy rightwards arrow straight infinity end subscript fraction numerator 2 space cos space x space sin space x over denominator 1 end fraction equals 2$

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