(a) limx→a[f(x)±g(x)] = limx→af(x)±limx→ag(x)(b) limx→a[cf(x)] =climx→af(x)Brett GeigerSection 1.4: Calculating Limits

Limit LawsLimit Laws:Supposecis a constant and limx→af(x) and limx→ag(x)exist. Then:(a) limx→a[f(x)±g(x)] = limx→af(x)±limx→ag(x)(b) limx→a[cf(x)] =climx→af(x)(c) limx→a[f(x)g(x)] = limx→af(x)·limx→ag(x)Brett GeigerSection 1.4: Calculating Limits

Limit LawsLimit Laws:Supposecis a constant and limx→af(x) and limx→ag(x)exist. Then:(a) limx→a[f(x)±g(x)] = limx→af(x)±limx→ag(x)(b) limx→a[cf(x)] =climx→af(x)(c) limx→a[f(x)g(x)] = limx→af(x)·limx→ag(x)(d) limx→af(x)g(x)=limx→af(x)limx→ag(x)if limx→ag(x)6= 0Brett GeigerSection 1.4: Calculating Limits

Limit LawsLimit Laws:Supposecis a constant and limx→af(x) and limx→ag(x)exist. Then:(a) limx→a[f(x)±g(x)] = limx→af(x)±limx→ag(x)(b) limx→a[cf(x)] =climx→af(x)(c) limx→a[f(x)g(x)] = limx→af(x)·limx→ag(x)(d) limx→af(x)g(x)=limx→af(x)limx→ag(x)if limx→ag(x)6= 0(e) limx→a[f(x)]n= (limx→af(x))nfor any rational numbernBrett GeigerSection 1.4: Calculating Limits

Limit LawsLimit Laws:Supposecis a constant and limx→af(x) and limx→ag(x)exist. Then:(a) limx→a[f(x)±g(x)] = limx→af(x)±limx→ag(x)(b) limx→a[cf(x)] =climx→af(x)(c) limx→a[f(x)g(x)] = limx→af(x)·limx→ag(x)(d) limx→af(x)g(x)=limx→af(x)limx→ag(x)if limx→ag(x)6= 0(e) limx→a[f(x)]n= (limx→af(x))nfor any rational numbern(f) limx→ac=cand limx→ax=aBrett GeigerSection 1.4: Calculating Limits

Evaluating Limits: Direct SubstitutionThe limit laws on the previous slide give nice properties of limits, butagain, how do we evaluate them in general?Brett GeigerSection 1.4: Calculating Limits

Evaluating Limits: Direct SubstitutionThe limit laws on the previous slide give nice properties of limits, butagain, how do we evaluate them in general? The most direct way, thoughit is not always applicable, is by just plugging in the approaching valueinto the function.Brett GeigerSection 1.4: Calculating Limits

Evaluating Limits: Direct SubstitutionThe limit laws on the previous slide give nice properties of limits, butagain, how do we evaluate them in general? The most direct way, thoughit is not always applicable, is by just plugging in the approaching valueinto the function.Direct Subbing:Iffis a polynomial, rational, or trig function andaisin the domain off, thenlimx→af(x) =f(a).Brett GeigerSection 1.4: Calculating Limits

Evaluating Limits: Direct SubstitutionThe limit laws on the previous slide give nice properties of limits, butagain, how do we evaluate them in general? The most direct way, thoughit is not always applicable, is by just plugging in the approaching valueinto the function.

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