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if f ‘(x) = x – 1/x^2 and f(1) = ½ find f(x)

if f ‘(x) = x – 1/x^2 and f(1) = ½ find f(x)

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question

f'(x) = x - \frac{1}{x^2}
\frac{df(x)}{dx} = x - \frac{1}{x^2}
df(x) = (x - \frac{1}{x^2})dx
\int df(x) = \int (x - \frac{1}{x^2})dx
f(x) = \frac{x^2}{2} + \frac{1}{x} + c
f(1) = \frac{1^2}{2} + \frac{1}{1} + c
\frac{1}{2} = \frac{1}{2} + 1 + c
c = -1
f(x) = \frac{x^2}{2} + \frac{1}{x} -1

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