The length of the subtangent to the curve sqr | vedclass

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Question

(D) Given the curve equation: $\sqrt{x} + \sqrt{y} = 3$.Differentiating both sides with respect to $x$:$\frac{1}{2\sqrt{x}} + \frac{1}{2\sqrt{y}} \cdo

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) Given the curve equation: $\sqrt{x} + \sqrt{y} = 3$.Differentiating both sides with respect to $x$:$\frac{1}{2\sqrt{x}} + \frac{1}{2\sqrt{y}} \cdot \frac{dy}{dx} = 0$.Rearranging to find $\frac{dy}{dx}$:$\frac{dy}{dx} = -\frac{\sqrt{y}}{\sqrt{x}}$.At the point $(4, 1)$,the slope $m$ is:$m = \left. \frac{dy}{dx} ight|_{(4, 1)} = -\frac{\sqrt{1}}{\sqrt{4}} = -\frac{1}{2}$.The length of the subtangent is given by the formula $\left| \frac{y}{dy/dx} ight|$.Substituting the values $y = 1$ and $\frac{dy}{dx} = -\frac{1}{2}$:$	ext{Length of subtangent} = \left| \frac{1}{-1/2} ight| = |-2| = 2$.

The length of the subtangent to the curve $\sqrt{x} + \sqrt{y} = 3$ at the point $(4, 1)$ is

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