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How to solve: $\lim\limits_{x \rightarrow 0} \frac{1-x^2}{\sqrt{1-4x^2}} = 4$
How to solve this problem: $\lim\limits_{x \rightarrow 0} \frac{1-x^2}{\sqrt{1-4x^2}} = 4$
A:
Hint: $1-4x^2$ is equal to $-x^2-5x^4+x^6$ (you can recognize this if you draw the function, by plotting $y=1-x^2$).
Remark: You could actually solve the problem directly, avoiding the asymptotic expansion:
Since $1-4x^2=-x^2(1+2x^2)$, taking the square root gives
$$
\sqrt{1-4x^2}=\pm \frac{x^2}{\sqrt{1+2x^2}}
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$$
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