Finding Integral Part of Numbers of the Form a^b Where a Is Irrational
If fx=x-x2+x3...
Question
If f(x)=x−x2+x3−x4⋯∞ and |x|<1, then f′(x)=
A
1(1+x)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1(1+x)2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
1(1−x)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1(1−x)2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B1(1+x)2 f(x)=x−x2+x3−x4+⋯∞
This is a G.P. with a=x,r=−x S∞=a1−r ⇒f(x)=x1+x ⇒f′(x)=(1+x)ddx(x)−xddx(1+x)(1+x)2 =1+x−x(1+x)2 =1(1+x)2