Let $ \mathrm{f}(x)=x+\frac{1}{2 x+\frac{1}{2 x+\frac{1}{2 x+\ldots \ldots . . \infty}}} . $ Then the value of $ f(100) . f^{\prime}(100) $ is

Question

Let $ \mathrm{f}(x)=x+\frac{1}{2 x+\frac{1}{2 x+\frac{1}{2 x+\ldots \ldots . . \infty}}} . $ Then the value of $ f(100) . f^{\prime}(100) $ is, $ 100 $, $ \frac{1}{100} $, $ -100 $, $ -\frac{1}{100} $

MARKS App · Accepted Answer

Let y = f x = x + 1 2 x + 1 2 x + 1 2 x + … … … ∞ ⇒ y = x + 1 x + y = x 2 + x y + 1 x + y ⇒ x y + y 2 = x y + x 2 + 1 ⇒ y 2 - x 2 = 1 Undefined y 2 = 1 + x 2 On differentiating ⇒ 2 y y ' = 2 x ⇒ y y ' = x ⇒ f 100 . f ' 100 = 100

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