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Question

# Statement I: If x=ey+ey+ey+…∞, then dydx=x1−xStatement II: If y=|cosx|+|sinx|, then the value of dydx at x=2π3 is (√3−12)Which of the above statement(s) is/are correct?

A
Statement I only
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B
Statement II only
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C
Both I and II
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D
Neither I nor II
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Solution

## The correct option is B Statement II onlyStatement I: x=ey+ey+ey+⋯∞⇒x=ey+xDifferentiating with respect to 'x', we get1=ey+x(1+y′)⇒1x−1=y′ (since ex+y=x)Hence, statement I is not correct.Statement II: y=|cosx|+|sinx|In the neighborhood of 2π3, cosx is negative and sinx is positive. Hence, |cosx|=−cosx and |sinx|=sinx.y=−cosx+sinx as x→2π3⇒y′=sinx+cosx⇒y′|x=2π3=√32−12Hence, only statement II is correct.

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