InterviewSolution
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InterviewSolution
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Let f(x) be a function such that its derovative f'(x) is continuous in [a, b] and differentiable in (a, b). Consider a function phi(x)=f(b)-f(x)-(b-x)f'(x)-(b-x)^(2)A. If Rolle's theorem is applicable to phi(x) on, [a,b], answer following questions. Let f(x)=sin x, a = alpha and b=alpha+h. If have exists a real number t such that 0lt t lt 1, phi'(alpha+th)=0 and (sin(alpha+h)-sinalpha-h cosalpha)/(h^(2))=lambdasin(alpha+th), then lambda= |
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Answer» `(1)/(2)` `THEREFORE""(sin (alpha+h)-sin alpha-h cos alpha)/(h^(2))=-(1)/(2)sin(alpha+th)` `therefore""alpha=-(1)/(2)` |
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