The lengths of tangent, subtangent, normal an | vedclass

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(D) Given curve is $y=x^2+x-1$ and point $(x_1, y_1)=(1,1)$.First, find the derivative: $\frac{dy}{dx} = 2x+1$.At $(1,1)$, the slope $m = \frac{dy}{dx

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$B, A, D, C$

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(D) Given curve is $y=x^2+x-1$ and point $(x_1, y_1)=(1,1)$.First, find the derivative: $\frac{dy}{dx} = 2x+1$.At $(1,1)$, the slope $m = \frac{dy}{dx} = 2(1)+1 = 3$.Length of tangent $A = \left|\frac{y_1 \sqrt{1+m^2}}{m}ight| = \left|\frac{1 \sqrt{1+3^2}}{3}ight| = \frac{\sqrt{10}}{3} \approx 1.054$.Length of subtangent $B = \left|\frac{y_1}{m}ight| = \frac{1}{3} \approx 0.333$.Length of normal $C = \left|y_1 \sqrt{1+m^2}ight| = |1 \sqrt{1+3^2}| = \sqrt{10} \approx 3.162$.Length of subnormal $D = |y_1 m| = |1 	imes 3| = 3$.Comparing the values: $B (0.333) Thus, the increasing order is $B, A, D, C$.

The lengths of tangent, subtangent, normal and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$ and $D$ respectively, then their increasing order is

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