Lt [1/x 1/ln(e^x -1) +(1/x) sinx -xlogx] (x>0,and [.] denotes x→0 greatest integer function)

Lt      [1/x1/ln(e^x-1)+(1/x)sinx-xlogx]  (x>0,and [.] denotes

x→0                                                        greatest integer    



1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear paidepelly

solve each part individually

first part

Lt x→0     1/x1/ln(e^x-1)


eLt x→0 -(ln x)/ln(ex-1)

use L hospital rule and find limit



for second part

Lt x→0(1/x)sinx

e Lt x→0sin x ln(1/x)

use L hospital rule and find limit 


for third part

Lt x→0-xlogx  =0

 Now add all three limit

  1/e +1+0

 =.367 +1+0 =1.367

so [1.367] =1 answer

Please feel free to post as many doubts on our discussion forum as you can.
 If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

 All the best.
Askiitians Experts

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy


Get your questions answered by the expert for free