28.Continuous:Note that g(0)5limx→01g(x)5limx→01cos x5cos (0)51, andlimx→02g(x)5limx→02(x1b)5b. We require limx→02g(x)5g(0),so b51. The function is continuous if b51.Differentiable:For b51, the left-hand derivative is 1 and the right-handderivative is 2sin (0)50, so the function is not differentiable. For other values of b, the function isdiscontinuous at x50 and there is no left-hand derivative. So, there is no value of bthat willmake the function differentiable at x50.29.Observe the pattern:}ddx}cos x5 2sin x}ddx55}cos x5 2sin x}ddx22}cos x5 2cos x}ddx66}cos x5 2cos x}ddx33}cos x5sin x}ddx77}cos x5sin x}ddx44}cos x5cos x}ddx88}cos x5cos xContinuing the pattern, we see that }ddxnn}cos x5sin xwhen n54k13 for any whole numberk. Since 99954(249)13,}ddx999999}cos x5sin x.30.Observe the pattern:}ddx}sin x5cos x}ddx55}sin x5cos x}ddx22}sin x5 2sin x}ddx66}sin x5 2sin x}d
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