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

The value of limy(1+xy)2y is

A
e2x
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
e2x
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
ex
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
ex
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A e2x
limy(l+xy)2y=z

Now, when limit are applied, it is of indeterminate form 1, so, writing it after applying log on both sides,

limy2ylog(1+xy)=logz

Now, LHS is of indeterminate form 0× as limy2y= and

limylog(1+xy)=0

So, Writing it as f(x)ϕ(x) where, f(x)=log(1+xy) and ϕ(x)=2y

limylog(1+xy)12y=logyz

Now, it is of indeterminate 00, So applying L Hospital Rule,

limy1(1+xy)(2xy2)(12y2)=logyz

limy2x(1+xy)=logyz

Now applying limit 2x(1+0)=logyz

2x=logyz

zy=e2x

Hence e2x is the correct option

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