The length of the subtangent at (2,2) to the | vedclass

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(B) Given the curve equation: $x^5 = 2y^4$. Differentiating both sides with respect to $x$: $5x^4 = 8y^3 \frac{dy}{dx}$ $\frac{dy}{dx} = \frac{5x^4}{8

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$8/5$

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(B) Given the curve equation: $x^5 = 2y^4$. Differentiating both sides with respect to $x$: $5x^4 = 8y^3 \frac{dy}{dx}$ $\frac{dy}{dx} = \frac{5x^4}{8y^3}$ At the point $(2,2)$, the slope of the tangent is: $\left(\frac{dy}{dx}ight)_{(2,2)} = \frac{5(2)^4}{8(2)^3} = \frac{5 	imes 16}{8 	imes 8} = \frac{80}{64} = \frac{5}{4}$. The formula for the length of the subtangent is given by $\left| \frac{y}{dy/dx} ight|$. Substituting the values: Length of subtangent $= \frac{2}{5/4} = 2 	imes \frac{4}{5} = \frac{8}{5}$.

The length of the subtangent at $(2,2)$ to the curve $x^5=2y^4$ is

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