If a curve passes through $(1,2)$ and has the slope of its tangent $1-\frac{1}{x^2}$ at a point $(x, y)$, then the equation of that curve is

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Aicharya · Accepted Answer

Given $\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{}$ $\begin{aligned} & \Rightarrow \int \mathrm{dy}=\int\left(1-\frac{1}{\mathrm{x}^2}ight) \mathrm{dx} \ & \Rightarrow \mathrm{y}=\mathrm{x}+\frac{1}{\mathrm{x}}+\mathrm{C} \end{aligned}$ Since y $(1)=2 \Rightarrow C=0$ $y(x)=x+\frac{1}{x}$

If a curve passes through $(1,2)$ and has the slope of its tangent $1-\frac{1}{x^2}$ at a point $(x, y)$,…

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