T_(x rarr(pi)/(2))[sec 3x cos 5x] -Turito

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Maths-

General

Easy

Question

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

$\frac{- 5}{3}$
$\frac{5}{3}$
$\frac{3}{5}$
$\frac{- 3}{5}$

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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