wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Evaluate:limx0xlogesinx


A

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

loge1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

loge1


Explanation for the correct option:

Finding the value of limx0xlogesinx

Step 1: Using the L' hospitality rule

Consider the given Equation as

I=limx0xlogesinxPuttingthelimitx0I=0logesin0I=0loge0I=0.indeterminentform

Using L'Hospital Rule,

limx0fxgx=limx0f'xg'x

So first we simplify the given Equation and then evaluate,

I=limx0xlogesinx

Rewriting xas11x

I=limx0logesinx1xI=logesin010I=indeterminentform

Step 2: Again, Using the L' hospitality rule

limx0fxgx=limx0f'xg'x

I=limx0logesinx1xI=limx0cosxsinx-1x2[Where,cosxsinx=cotx]I=limx0cotx1-x2[Where,cotx=1tanx]I=limx0-xtanxx[where,limx0tanxx=1]I=limx0-xI=0I=loge1[Where,loge1=0]

Hence, option (B) is the correct answer.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon