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Maths-

General

Easy

Question

$L t left parenthesis x rightwards arrow pi divided by 2 right parenthesis left square bracket s e c 3 x c o s 5 x right square bracket$

$(- 5) / 3$
$(5) / 3$
$3 / 5$
$- 3 / 5$

hint Hint:

In this question first we will rearrange the expression using $sec open parentheses x close parentheses equals fraction numerator 1 over denominator cos open parentheses x close parentheses end fraction$ and then we will use the formula $limit as x minus greater than pi over 2 of fraction numerator cos open parentheses x close parentheses over denominator x end fraction equals 1$ .

The correct answer is: $left parenthesis negative 5 right parenthesis divided by 3$

In this question we have find the limit of $sec open parentheses 3 x close parentheses cos open parentheses 5 x close parentheses$
Step1: Rearranging the expression
We know that $sec open parentheses x close parentheses equals fraction numerator 1 over denominator cos open parentheses x close parentheses end fraction$ . So, the equation changes to
$limit as x minus greater than pi over 2 of fraction numerator cos open parentheses 5 x close parentheses over denominator cos open parentheses 3 x close parentheses end fraction$
Step2: Finding the limit.
We know that $limit as x minus greater than pi over 2 of fraction numerator cos open parentheses x close parentheses over denominator x end fraction equals 1$
By multiplying both numerator and denominator by $3 x$ and $5 x$ .
=> $limit as x minus greater than pi over 2 of fraction numerator cos open parentheses 5 x close parentheses cross times 3 x cross times 5 x over denominator cos open parentheses 3 x close parentheses cross times 3 x cross times 5 x end fraction$
Step3: Rearranging the equation.
=> $limit as x minus greater than pi over 2 of fraction numerator begin display style fraction numerator cos open parentheses 5 x close parentheses over denominator 5 x end fraction end style cross times 5 x over denominator begin display style fraction numerator cos open parentheses 3 x close parentheses over denominator 3 x end fraction end style cross times 3 x end fraction$
=> The expression changes as follows
=> $limit as x minus greater than pi over 2 of fraction numerator 5 x over denominator 3 x end fraction$
=> $limit as x minus greater than pi over 2 of 5 over 3 equals 5 over 3$ .
So, the value of the limit is $5 over 3$ .

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