Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • For n belong to N fn(x)=tan x/2 (1+sec x)(1+sec 2x)(1+sec4x).........(1+sec 2^n x) Then lim fn(x)/2x is equal to

For n belong to N fn(x)=tan x/2 (1+sec x)(1+sec 2x)(1+sec4x).........(1+sec 2^n x) Then lim fn(x)/2x is equal to

Answers (1)

best_answer

Solution:  We have , nin N

                 f_n(x)= an fracx2(1+sec x)(1+sec 2x)(1+sec 4x)........(1+sec 2^xx)

      \ \ Rightarrow f_n(x)= an fracx2(frac1+cos xcos x)(1+sec 2x)(1+sec 4x)........(1+sec 2^nx)\ \ = an x (frac1+cos 2xcos 2x)(1+sec 4x).........(1+sec 2^nx)\ \ = an 2x (1+sec 2^2x)........(1+sec 2^nx)\ \ = an 2^n-1x(1+sec 2^nx)= an 2^nx  

Now ,       lim_x o 0fracf_n(x)2x=lim _x o 0frac an 2^nx2^nxcdot 2^n-1=2^n-1

Posted by

Deependra Verma

View full answer

Similar Questions

Latest Question