Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

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

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

hint Hint:

We are given a function to find a limit. Before substituting the value of the limit, we should make sure we don’t get zero value.

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

The given function is
$limit as x rightwards arrow pi over 2 of s e c 3 x cos 5 x space equals stack lim space space with x rightwards arrow pi over 2 below fraction numerator c o s 5 x over denominator cos 3 x end fraction space space space space space space space space space space space space space space space space space space space space space space W h e n space p u t space t h e space v a l u e space o f space x rightwards arrow pi over 2 T h e n space t h e space f u n c t i o n space i s space 0 over 0 S o comma space w e space w i l l space u s e space L apostrophe H o s p i t a l space R u l e s space space space space space space limit as x rightwards arrow straight pi over 2 of fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction space equals limit as x rightwards arrow straight pi over 2 of fraction numerator f apostrophe left parenthesis x right parenthesis over denominator g apostrophe left parenthesis x right parenthesis end fraction space$
$limit as x rightwards arrow pi over 2 of f left parenthesis x right parenthesis space equals limit as x rightwards arrow straight pi over 2 of fraction numerator 5 sin 5 x over denominator 3 sin 3 x end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 5 sin 5 begin display style straight pi over 2 end style over denominator 3 sin 3 begin display style straight pi over 2 end style end fraction space space space space space space space space N o w comma space space sin fraction numerator 5 straight pi over denominator 2 end fraction equals sin left parenthesis 2 straight pi plus straight pi over 2 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals sin straight pi over 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 space space space space space space space space space space space space space sin fraction numerator 3 straight pi over denominator 2 end fraction space equals space sin left parenthesis straight pi space plus space straight pi over 2 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals sin straight pi over 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1$
$limit as x rightwards arrow pi over 2 of f open parentheses x close parentheses equals fraction numerator 5 open parentheses 1 close parentheses over denominator 3 open parentheses 1 close parentheses end fraction equals 5 over 3$
This is the final answer.

For such questions, we should know different formulas of limits. We should know L'Hospitals rule to solve question.

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.