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Let f(x)=x+1/(2x+1/(2x+1/(2x+oo))) Com...

Let `f(x)=x+1/(2x+1/(2x+1/(2x+oo)))` Compute the value of `f(50)dotf^(prime)(50)`

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`f(x)=x + (1)/(x + x + (1)/(2x + (1)/(2x + .....oo)))=x+(1)/(x+f(x))`
`"or "f(x)-x=(1)/(x+f(x))`
`"or "f^(2)(x)-x^(2)=1`
Differentiating w.r.t. x, we get
`"or "2f(x)cdotf'(x)-2x=0`
`"or "f(x)cdotf'(x)=x`
`"or "f(50)cdotf'(50)=50`
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