plz solve -


Lt(x->0) (log(cos x)/(sinx)^2)


thanx in advance..

2 years ago

Share

Answers : (2)

                    

Lt x->0 log(cos x)/ (sinx)2


Lt x->0 log [1 + (cosx - 1)]/(sinx)2                                         {Add and subtract 1}


Lt x->0 log [1 + (cosx - 1)](cosx - 1)/ (cosx - 1) (sin x)2          {Multiply divide by (cosx - 1)}


Lt x->0 {log [1 + (cosx - 1)]/ (cos x - 1)}  {(cosx - 1) / (sinx)2}


Lt x->0 {(log [1 + m])/ (m)} { - (1 - cosx)/ ??(sinx)2}


 Here m->0 as cosx - 1 ->0 when x-> o So, Standard limit Lt x->0  log[ 1 + x]/ x = 1


Lt x->0 {1} {- (1 - cosx)(x2) / (x2) (sinx)2                                            {Multiply divide by (sinx)2}


Lt x->0 - {(1- cosx) / (x2)} { (x2) / (sinx)2}


Using Standard limit Lt x->0 (1-cosx) / (x2) = 1/2 and Lt x->0  (x/ sinx)= 1, we get,


Lt x->0 - {1/2} { (1)2 }


Lt x->0 -1/2


= -1/2

2 years ago
                    

Anmol , Ur answer is indeed right . but I want to do it by a simple method called L Hopitals rule.


Any problem yielding 0/0 by direct substition can be solved by the approach.


This method coveys tht any  limit yielding 0/0


lim f(x)/g(x) = {d f(x) /dx } / {d g(x) /dx }


Here in the question by direct substitution we get 0/0 So apply L Hopitals rule


Lt (x->0) log(cos(x))/(sinx)2 = Lt(x->0)d/dx {log(cos(x))} / d/dx {sin2x} = -1/2 cos2(x)  = -1/2 (By direct Substitution)

2 years ago

Post Your Answer

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
Consider a series of `n` concentric circles C(1),C(2),C(3), ....., C(n) with radii r(1),r(2),r(3), ......., r(n) respectively, satisfying r(1)>r(2)>r(3).... > r(n) & r(1)=10. The circles are...
 
 
Hi consider making the diagram yourself you must know that c(n) is the innermost circle i'm assuming tangents form c(i) to c(i+1) of which chord of contact touches c(i+2) try to understand...
  img
Arun Kumar one month ago
 
Hi Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty
  img
Arun Kumar one month ago
 
Hello Thanks & Regards Arun Kumar Btech, IIT Delhi Askiitians Faculty
  img
Arun Kumar one month ago
Find the no. Of solution of equation x 2 =2 x . Please reply and send solutions to mobie number +919587748173. Thank u.
 
 
Hi Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty
  img
Arun Kumar one month ago
 
If x>0, then consider the function, f(x) = x 1/x . This is monotonic in the intervals (0, e) and (e, infty) Thus only two solutions exist to x 1/x =2 1/2 i.e. x =2 and x=4 If x x – x 2...
 
mycroft holmes one month ago
 
 
palak singhal one month ago
what is (x+3)(x -2)??
 
 
Hello Student, Please find the answer to your question (x + 3)(x – 2) = x^2+x-6 Hope that you will be satisfied with this
  img
Pankaj 19 hours ago
 
x(x – 2) + 3(x – 2) = x^2 – 2x + 3x – 6 = X^2 + x – 6 Hope that you will understand now Thanks
  img
Pankaj 19 hours ago
 
ok. But can you show me the steps also.
 
Bhawna 19 hours ago
 
Sir, what type of question is this? Can you explain this to me?
 
13 hours ago
 
Hi Siddharth, This is multiplication of linear factors
 
13 hours ago
 
yes sir. Thank you
 
13 hours ago
View all Questions »