LimitsLimit exists, function not exist-1 1 2 3 4 5 6-112345LimitsLimit=function ⇒ continuous-1 1 2 3 4 5 6-112345LimitsLimit 6= function ⇒ not continuous-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-4-3-2-112345678910LimitsLimits and continuous functionsIIf f(x) is continuous at x = a then thelimx→af(x) = f(a)Ithis means that if a f(x) is continuous at x = a then to findthe limit of f(x) at x = a you only need to evaluate f(x) atx = a.Ii.e. to find limx→af(x) when f(x) is continuous at x = a justfind f(a).Ipolynomials are smooth, continuous functions for all x so thismethod can be used with polynomials. If P(x) is a polynomialthen:limx→aP(x) = P(a)LimitsLimits and continuous functionsIIf f(x) is continuous at x = a then thelimx→af(x) = f(a)Ithis means that if a f(x) is continuous at x = a then to findthe limit of f(x) at x = a you only need to evaluate f(x) atx = a.Ii.e. to find limx→af(x) when f(x) is continuous at x = a justfind f(a).Ipolynomials are smooth, continuous functions for all x so thismethod can be used with polynomials. If P(x) is a polynomialthen:limx→aP(x) = P(a)LimitsLimits and continuous functionsIIf f(x) is continuous at x = a then thelimx→af(x) = f(a)Ithis means that if a f(x) is continuous at x = a then to findthe limit of f(x) at x = a you only need to evaluate f(x) atx = a.Ii.e. to find limx→af(x) when f(x) is continuous at x = a justfind f(a).Ipolynomials are smooth, continuous functions for all x so thismethod can be used with polynomials. If P(x) is a polynomialthen:limx→aP(x) = P(a)LimitsLimits and continuous functionsIIf f(x) is continuous at x = a then thelimx→af(x) = f(a)Ithis means that if a f(x) is continuous at x = a then to findthe limit of f(x) at x = a you only need to evaluate f(x) atx = a.Ii.e. to find limx→af(x) when f(x) is continuous at x = a justfind f(a).Ipolynomials are smooth, continuous functions for all x so thismethod can be used with polynomials. If P(x) is a polynomialthen:limx→aP(x) =