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If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=...

If `y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3` is `(1-sqrt(3))/2` (b) 0 (c) `1/2(sqrt(3)-1)` (d) none of these

A

`(1-sqrt(3))/(2)`

B

0

C

`(sqrt(3)-1)/(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
In the neighbourhood of `x=(2pi)/(3)`, we have
`cosxlt0" and "sinxgt0`
`implies" "cosx|=-cosx" and "|sinx|=sinx`
`:." "y=|cosx|+|sinx|`.
`implies" "y=-cosx+sinx`
`implies" "(dy)/(dx)=sinx+cosx`
`implies" "((dy)/(dx))_(x=(2pi)/(3))="sin"(2pi)/(3)+"cos"(2pi)/(3)=(sqrt(3)-1)/(2)`
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