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Question

L t subscript x not stretchy rightwards arrow pi over 2 end subscript left square bracket sec space 3 x cos space 5 x right square bracket

  1. fraction numerator negative 5 over denominator 3 end fraction
  2. 5 over 3
  3. 3 over 5
  4. fraction numerator negative 3 over denominator 5 end fraction

Hint:

In this question, we will use L;' Hospital theorem and simplify it and put the value of x.

The correct answer is: fraction numerator negative 5 over denominator 3 end fraction


    equals limit as x rightwards arrow bevelled straight pi over 2 of space open parentheses fraction numerator cos space 5 x over denominator cos space 3 x end fraction close parentheses
U sin g space L apostrophe H o s p i t a l space t h e o r e m comma
equals limit as x rightwards arrow bevelled straight pi over 2 of space space fraction numerator begin display style fraction numerator d blank over denominator d x end fraction open parentheses cos space 5 x close parentheses end style over denominator begin display style fraction numerator d blank over denominator d x end fraction open parentheses cos space 3 x close parentheses end style end fraction
equals limit as x rightwards arrow bevelled straight pi over 2 of space space fraction numerator negative left parenthesis sin space 5 x right parenthesis.5 over denominator negative left parenthesis sin space 3 x right parenthesis.3 end fraction
equals 5 over 3 space. limit as x rightwards arrow bevelled straight pi over 2 of space fraction numerator sin space 5 x over denominator sin space 3 x end fraction
equals 5 over 3 cross times fraction numerator sin space 5 cross times begin display style straight pi over 2 end style over denominator sin space 3 cross times begin display style pi over 2 end style end fraction
equals 5 over 3 cross times fraction numerator sin space 450 degree over denominator sin space 270 degree end fraction
equals 5 over 3 cross times fraction numerator 1 over denominator negative 1 end fraction
equals fraction numerator negative 5 over denominator 3 end fraction.

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