A) 2
B) \[\frac{1}{2}\]
C) 0
D) 1
Correct Answer: D
Solution :
\[\left| f\left( x \right)-f\left( y \right) \right|\le \,\,2{{\left[ x-y \right]}^{3/2}}\] \[\underset{y\,\to \,x}{\mathop{\lim }}\,\left| \frac{f(x)\,-\,f(y)}{x-y} \right|\,\,\le \,\,\underset{y\,\to \,x}{\mathop{\lim }}\,\,\,2\,{{\left| x-y \right|}^{1/2}}\] \[\Rightarrow \,\,\,\left| f'(x) \right|\,\,\le \,\,0\Rightarrow \,\,{f}'(x)\,\,=\,\,0\] \[\Rightarrow \,\,\,\,f\left( x \right)=constant\] \[as\text{ }f\left( 0 \right)=1\,\,\Rightarrow \,\,f\left( x \right)=1\] \[\int\limits_{0}^{1}{{{f}^{2}}(x)\,dx\,\,=\,\,1}\]You need to login to perform this action.
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