Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
plz solve -
Lt(x->0) (log(cos x)/(sinx)^2)
thanx in advance..
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
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)
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !