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. 1
  2. 0
  3. -1
  4. straight infinity

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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