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Question
Given that `1/y + 1/x = 1/12` and y decreases at a rate of 1 cms–1, find the rate of change of x when x = 5 cm and y = 1 cm.
Solution
Given, `dy/dt` = 1 cm/s
And `1/y + 1/x = 1/12`
On differentiating w.r.t 't' on both sides, we get
`(-1)/y^2 dy/dt - 1/x^2 dx/dt = 0`
Put x = 5, y = 1 and `dy/dt = 1`
∴ `(-1)/1^2 xx 1 - 1/5^2 xx dx/dt = 0`
`\implies - 1 - 1/25 dx/dt = 1`
`\implies (-1)/25 dx/dt = 0`
`\implies dx/dt = - 25`
Hence, the rate of change of 'x' is – 25 cm/sec.
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