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Soln: Basic concepts(i) lim_(x rarr c)f(x) exist and equal to l if and only if lim_(x rarrC^(-))f(x)=lim_(x rarrC^(+))f(x)=l in this case we writelim_(x rarrC^(-))f(x)=lim_(x rarrc^(+))f(x)=lim_(x rarr c)f(x)=l.Given the graph isNo Klim_(x rarr1^(-))f(x)=2, since in the graph of f(x) if we approach the point x=1 from left side the graph of f(x) tends to 2 .and lim f(x)=2, since in the graph of f(x) x rarr1^(+)if we approach the point x=1 from rigth side the graph of f(x) tends to 2 .since lim_(x rarr1^(-))f(x)=lim_(x rarr1^(+))f(x)=2; then lim_(x rarr1^(-))f(x) existand lim_(x)f(x)=2Thus lim_(x rarr1)f(x)=2 x rarr1Againlim_(x rarr1^(-))g(x)=2; since in the graph of g(x) ... See the full answer