lim x-->0 [cos(sinx)-cosx] / x4



ans: 1/6

2 years ago

Share

Answers : (3)

                                        

Using L Hopitals rule


lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d/dx[cos(sin(x))-cos(x)]/x^4 if ([cos(sin(x))-cos(x)]=0 and x=4)


Again since the expression is yielding 0/0 appyling L hopitals rule, 


lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d2/dx2[cos(sin(x))-cos(x)]/x^4 at x=0


Again since the expression is yielding 0/0 appyling L hopitals rule, 


lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d3/dx3[cos(sin(x))-cos(x)]/x^4 at x=0


Again since the expression is yielding 0/0 appyling L hopitals rule, 


lim x tends to 0 [cos(sin(x))-cos(x)]/x^4 = d4/dx4[cos(sin(x))-cos(x)]/x^4 at x=0


Now Since the expression 4/24= 1/6 .


Hence 1/6 is the answer 


 



2 years ago
                                        

lim[cos(sinx)-cosx]/x^4


=lim[-sin(sinx)cosx+sinx]/(4x^3)


=lim[sin(sinx)sinx-cos(sinx)cos2x+cosx]/12x2


=lim[cosx-cos(sinx)cos2x]/12x2


=lim[1-cos(sinx)cosx]/12x2


=lim[sin(sinx)cos2x+cos(sinx)sinx]/24x


differentiate once more w.r.t. to get the answer


Dear Moderator: If I need to provide any more details, please contact me at <mn_chetan@yahoo.com

2 years ago
                                        

thanks a lot

2 years ago

Post Your Answer

More Questions On IIT JEE Entrance Exam

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
which book i read?
 
 
Hi, If you feel you have a good intellectual level, then follow arihant books, otherwise just follow your text books and take some study material for the support....
  img
Shobhit Varshney yesterday
i need suggestions for my preparation?
 
 
sir the time you have contacted me once, i was not present at that time. kindly ignore it .
 
k m vamsi 3 months ago
Sir what are the chances of seat upgradation in 2 nd or 3 rd round of Jee Adv counselling this year?
 
 
I’m from OBC cat . category rank 1585. and I got Mech in IIT patna in 1 st round.
 
Ashish Kumar Yadav 3 months ago
Hi my son has got state rank 8041 and general category rank 42950. will he be able to get a seat in other than home state nits?
 
 
Hi, There are very less chances of you getting a NIT seat. For a better estimation refer last years opening and cloasding rank ! You can also visit askIITaisn college and branch predictor...
  img
Yash Baheti 3 months ago
The graph of the function y=cosxcos(x+2)-cos^2(x+1)is
 
 
your question is not clear, please rewrite it.
 
Chirag Goel 7 days ago
 
your question is not clear.
 
Chirag Goel 7 days ago
Sir, I am provided with just SC Merit List Ranking, and not All India Rank. Why? Will there be any kind of problem for the admiisions in IITs? And also, I want to know how much marks have I...
 
 
No, most of the sc category students are not eligible for all india rank , so there will be no problem for you, this will be given in your score card .
  img
Sher Mohammad 3 months ago
View all Questions »