I am having trouble with a homework question that seems really simple, and I get the wrong answer.
$\lim_{x\to 0} \frac{\sqrt{1+2x}-\sqrt{1-4x}}{x}$
I then get the derivative of the top and bottom and I get
$(1+2x)^{\frac{-1}{2}} - 2(1-4x)^\frac{-1}{2}$
Plugging in $0$ gives me $-1$ and I am not sure why my answer doesn't match the book’s answer of $3$. I can rarely get the answer from the book so I just assume that the author does not really expect you to get the answer on your own.