a lim x a f x g x lim x a f x lim x a g x b lim x a cf x c lim x a f x Brett

# A lim x a f x g x lim x a f x lim x a g x b lim x a

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(a) limxa[f(x)±g(x)] = limxaf(x)±limxag(x)(b) limxa[cf(x)] =climxaf(x)Brett GeigerSection 1.4: Calculating Limits
Limit LawsLimit Laws:Supposecis a constant and limxaf(x) and limxag(x)exist. Then:(a) limxa[f(x)±g(x)] = limxaf(x)±limxag(x)(b) limxa[cf(x)] =climxaf(x)(c) limxa[f(x)g(x)] = limxaf(x)·limxag(x)Brett GeigerSection 1.4: Calculating Limits
Limit LawsLimit Laws:Supposecis a constant and limxaf(x) and limxag(x)exist. Then:(a) limxa[f(x)±g(x)] = limxaf(x)±limxag(x)(b) limxa[cf(x)] =climxaf(x)(c) limxa[f(x)g(x)] = limxaf(x)·limxag(x)(d) limxaf(x)g(x)=limxaf(x)limxag(x)if limxag(x)6= 0Brett GeigerSection 1.4: Calculating Limits
Limit LawsLimit Laws:Supposecis a constant and limxaf(x) and limxag(x)exist. Then:(a) limxa[f(x)±g(x)] = limxaf(x)±limxag(x)(b) limxa[cf(x)] =climxaf(x)(c) limxa[f(x)g(x)] = limxaf(x)·limxag(x)(d) limxaf(x)g(x)=limxaf(x)limxag(x)if limxag(x)6= 0(e) limxa[f(x)]n= (limxaf(x))nfor any rational numbernBrett GeigerSection 1.4: Calculating Limits
Limit LawsLimit Laws:Supposecis a constant and limxaf(x) and limxag(x)exist. Then:(a) limxa[f(x)±g(x)] = limxaf(x)±limxag(x)(b) limxa[cf(x)] =climxaf(x)(c) limxa[f(x)g(x)] = limxaf(x)·limxag(x)(d) limxaf(x)g(x)=limxaf(x)limxag(x)if limxag(x)6= 0(e) limxa[f(x)]n= (limxaf(x))nfor any rational numbern(f) limxac=cand limxax=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, thenlimxaf(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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• Spring '08
• Xu
• Continuous function, Limit of a function, Multiplicative inverse, Brett Geiger