If y=1+1x+1x2+1x3+….∞ with |x|>1, then dydx is equal to:
x2y2
y2x2
-y2x2
Explanation for the correct option.
Step 1: Simplify the given equation.
1+1x+1x2+1x3+….∞ are in infinite G.P, where a=1andr=1x.
Sum of infinite terms of G.P =a1-r.
So,
y=11-1x=xx-1.....1
Step 2: Find dydx.
By differentiating w.r.t x, we get
dydx=x-11-x1x-12=x-1-xx-12=-1x-12=-1xy2from1=-y2x2
Hence, option D is correct.
loge(n+1)−loge(n−1)=4a[(1n)+(13n3)+(15n5)+...∞] Find 8a.
If f=x1+x2+13(x1+x2)3+15(x1+x2)5+... to ∞ and g=x−23x3+15x5+17x7−29x9+..., then f=d×g. Find 4d.