Maths-
General
Easy

Question

L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style a x over denominator x cos space x end fraction

  1. 1
  2. 0
  3. a
  4. none of these

Hint:

In the question we will first 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 open parentheses x close parentheses end fraction. Then we will put the value of x.

The correct answer is: a


    L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator sin begin display style space end style a x over denominator x cos space x end fraction
u sin g space space L space 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 sin begin display style space end style a x over denominator begin display style fraction numerator d blank over denominator d x end fraction end style x cos space x end fraction
equals L t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator a space cos space a x over denominator negative x sin x plus cos x end fraction
equals fraction numerator a space cos left parenthesis a cross times 0 right parenthesis over denominator negative 0 sin 0 plus cos 0 end fraction
equals fraction numerator a over denominator 0 plus 1 end fraction
equals a

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