Prove that the below equation has a root in the given interval: cos(sqrt x)=e^x−2 in the interval (0,1)." So I found that f(1)=0.54 and f(0)=1 for the left hand side. But this did not seem to be the same as the right hand side. So how exactly can I prove it is continuous in the interval, and possibly go further and prove the presence of a root?

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