A) \[-\frac{3}{2}\]
B) \[\frac{3}{2}\]
C) \[\frac{5}{2}\]
D) \[-\frac{5}{2}\]
Correct Answer: A
Solution :
Slope \[=\frac{dy}{dx}=1-\frac{1}{{{x}^{2}}}\] \[\Rightarrow\] \[\int_{{}}^{{}}{dy}=\int_{{}}^{{}}{\left( 1-\frac{1}{{{x}^{2}}} \right)dx}\] \[\Rightarrow\] \[y=x+\frac{1}{x}+C,\] which is the equation of the curve since curve passes through the point \[\left( 2,\frac{7}{2} \right)\] \[\therefore\] \[\frac{7}{2}=2+\frac{1}{2}+C\Rightarrow C=1\] \[\therefore\] \[y=x+\frac{1}{x}+1\] when \[x=-2,\] then \[y=-2+\frac{1}{-2}+1=\frac{-3}{2}\]
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