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
(1 -w -w²) 5 = 32
 
 
Hii shah as you know 1 + w +w ² = 0 whem w is cube root of unity.hence you can write it as -w -w² = 1 therefore 2^5 is 32.. . . . . . . . ….. . . . .
  img
Sourabh Singh one month ago
A= 1 101 +2 101 +3 101 + 4 101 +......+34 101 . Find the remainder when A is divided by 70.
 
 
Hi, This question can be easily solved by using binomial theorem. Write 1 as 7-6 two as 7-5 and so on, remember that 7 multiple will be 7 and 8 will be written as 7+1 and so on. Now when you...
  img
Yash Baheti one month ago
see attachment and explain it
 
 
Approach: we’ll first satisfy the condition given in the question. Answer: For filling each row with four letters taken at random, choices are 4. So in 4! ways. Now, we are free to...
  img
Ravi 2 months ago
integrate, ∫ X X dx
 
 
Ans: Hello Student, Please find answer to your question below There is not any standard mathematical expression for this integral. What we can do is expand the integral function around zero...
  img
Jitender Singh 4 months ago
Let f : A-> A where A = { 1, 2, 3, 4, 5} such that ff(x) = x . How many such functions are possible
 
 
First note that the function is injective: f(x) = f(y) implies f(f(x)) = f(f(y)) which yields x = y. We say that a number x is fixed by f if f(x) = x. Now, if f(a) = b, with a and b unequal,...
 
mycroft holmes 2 months ago
 
In general the real functions which satisfies the condition that fof(x) = x are (i) f(x) = a – x where a is any real no. (ii) f(x) = x But here, f: A → A is the function which should satisfy...
 
Y RAJYALAKSHMI 3 months ago
 
Pl. ignore this solution – it is incomplete
 
Y RAJYALAKSHMI 3 months ago
root 2 cosx+ root6 sinx= max (sintheta + costheta) where theta belongs to R find the general value of x
 
 
Ans:Hello student, please find answer to your question
  img
Jitender Singh 5 months ago
 
thnk u very much
 
keerthi priya 4 months ago
View all Questions »