1.Let f:R→Rf:\mathbb R\to\mathbb Rf:R→R be such that limx→∞f(x)=M>0\displaystyle\lim_{x\to\infty}f(x)=M>0x→∞limf(x)=M>0. Then which of the following is false?a.limx→∞xsin(1/x)f(x)=M\displaystyle\lim_{x\to\infty}x\sin(1/x)f(x)=Mx→∞limxsin(1/x)f(x)=Mb.limx→∞sin(f(x))=sinM\displaystyle\lim_{x\to\infty}\sin(f(x))=\sin Mx→∞limsin(f(x))=sinMc.limx→∞xsin(e−x)f(x)=M\displaystyle\lim_{x\to\infty}x\sin(e^{-x})f(x)=Mx→∞limxsin(e−x)f(x)=Md.limx→∞sinxxf(x)=0\displaystyle\lim_{x\to\infty}\frac{\sin x}{x}f(x)=0x→∞limxsinxf(x)=0Login to continueOnly logged in users canattempt or see the solution.
