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Q9Section I (General (compulsory))9 of 180

Uniform continuity — checking three named functions

Suppose that f1,f2,f3f_1,f_2,f_3 are functions defined by f1(x)=x2,0≤x<∞f_1(x)=x^2, 0\le x<\infty; f2(x)=cos⁡(x),0≤x≤π/2f_2(x)=\cos(x), 0\le x\le\pi/2; and f3(x)=sin⁡(x)/xf_3(x)=\sin(x)/x for x≠0x\neq0, f3(0)=1f_3(0)=1. Which of the above functions is/are uniformly continuous on their respective domains?

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