The equation of curve passing through $\left(2, \frac{7}{2}\right)$ and having slope $1-\frac{1}{x^2}$ at (x, y) is :
Answer & explanation
Correct answer: option 3
$\frac{d y}{d x}=1-\frac{1}{x^2} \Rightarrow y=x+\frac{1}{x}+c$
At $(2,7 / 2) \frac{7}{2}=2+\frac{1}{2}+c \Rightarrow c=1$
Therefore $y=x+\frac{1}{x}+1 \Rightarrow xy=x^2+x+1$
Hence (3) is the correct answer.