1.

यदि `y=sqrt(x+sqrt(x+sqrt(x+….oo)))`, तो सिद्ध कीजिए कि `(2y-1)(dy)/(dx)=1.`

Answer» `y=sqrt(x+sqrt(x+sqrt(x+….oo)))`
`y=sqrt(x+y)" "rArr" "y^(2)=x+y`
`rArr" "2y(dy)/(dx)=1+(dy)/(dx)`
`rArr" "(2y-1)(dy)/(dx)=1` यही सिद्ध करना था ।


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