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
If a 1 , a 2 ,a 3 , a 4 , a 5 , a 6 are in A.P., then prove that the system of equations a 1 x + a 2 y = a 3 , a 4 x + a 5 y = a 6 is consistent
 
 
Let a 1 = a, then a 2 = a + d, a 3 = a + 2d, a 4 = a + 3d, a 5 = a + 4d, a 6 = a + 5d The equations are consisent if a 4 /a 1 # a 5 /a 2 => a 4 * a 2 # a 5 * a 1 => (a + 3d) * ( a + d) # (a...
 
Y RAJYALAKSHMI 2 days ago
Let a,b,c E R and a (is not equal to 0) be such that (a+c) 2 2, then the quadratic equation ax 2 + bx + c = 0 has : Imaginary roots. Real roots. Exactly one real root lying in the...
 
 
Hello student, Please find my response to your question below Iam unable to interpret your query Because you didot mention the condition clearly here so without condition you may not get an...
  img
SHAIK AASIF AHAMED 6 days ago
 
Hello student, Please find my response to your question below What does the line’a (is not equal to 0) be such that (a+c) 2 ’mean it does not have a meaning i think there should...
  img
SHAIK AASIF AHAMED 5 days ago
 
in the first line it is (a+c)^2
 
Ujjwal 5 days ago
If the equation x^2 – x – p =0 and x^2 - 2xp - 12 =0 have a common root ,find it
 
 
x^2-x-p=0; p = (-x^2 +x) substitute p in 2 nd equation x^2-2x(-x^2+x)-12=0 2x^3-x^2-12=0 solving this eqn we get x = 2 and other roots are unreal so, the common root is 2
 
Y RAJYALAKSHMI one month ago
Please solve this ∫e x tanx(1-2sec 2 x) dx I am waiting for your reply
 
 
Ans:Hello student, please find answer to your question
  img
Jitender Singh one month ago
find dy/dx when y= (sin^-1 (x))^x + x^x
 
 
Ans: Hello Student, Please find answer to your question below Now simply apply the chain rule
  img
Jitender Singh 18 days ago
CARBON IS PRESENT AS GRAPHITE IN WHITE CAST IRON
 
 
Cast iron is iron or a ferrous alloy which has been heated until it liquefies, and is then poured into a mould to solidify. It is usually made from pig iron. The alloy constituents affect...
 
sanjay sanjeev patro one year ago
 
carbon is present as cementite(Fe3C) in white cast iron.............where as in grey cast iron it is present as Graphite........hope you understand......
 
saisandeep Mattaparthi one year ago
 
you are right, carbon is present as graphite in white cast iron for inthe time of extraction and acts as cathode
 
reddy RGUKT(NUZVID) one year ago
View all Questions »