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not continuous at `x=pi//2`continuous but not differentiable at x=0 neither continuous nor differentiable at `x=pi//2`none of these

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We have <br> `f(x)=min {1,cosx,1-sin x}` <br> `Rightarrow f(x)={{:(,cos x,-pi//2 le x le 0),(,1-sin x,0 lt xle pi//2),(,cos x, pi//2 lt x le pi):}` <br> We find that <br> `underset(x to 0^(-))lim f(x)=underset(x to 0^(-))lim cos x=1` <br> `underset(x to 0^(+))lim f(x)=underset(x to 0)lim 1-sinx=1`<br> `and f(0)=cos 0=1` <br> `therefore underset(x to 0^(-))lim f(x)=underset(x to 0^(+))lim f(x)=f(0)` <br> So, f(x) is continuous at x=0 <br> Now, <br> `("LHD at x=0")=((d)/(dx)(cos x))_(x=0)=0` <br> `("RHD at x=0")=((d)/(dx)(1-sin x))_(x=0)=-1` <br> `therefore ("LHD at x=0") ne ("RHD at x=0")` <br> Hence, f(x) is not differentiable at x=0. However it is continuous there at. <br> At `x=pi//2` also, f(x) is continuous but not differentiable