If $m$ is the slope of a tangent to the curve $e^{2 y} = 1 + 4 x^{2}$ then

$| m | < 1$

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$| m | \geq 1$

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$| m | > 1$

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$| m | \leq 1$

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Solution

The correct option is D
$| m | \leq 1$

Taking $log$ on both the sides, we get

$2 y = log (1 + 4 x^{2})$

Differentiating with respect to $x$ , we get

$2 \frac{d y}{d x} = \frac{8 x}{1 + 4 x^{2}}$

$\Rightarrow \frac{d y}{d x} = \frac{4 x}{1 + 4 x^{2}}$

Since, $4 x \leq 1 + 4 x^{2}$ so $| m | \leq 1$

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