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

This preview shows page 10 - 19 out of 54 pages.

(a) limxa[f(x)±g(x)] = limxaf(x)±limxag(x)(b) limxa[cf(x)] =climxaf(x)Brett GeigerSection 1.4: Calculating Limits
Background image
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
Background image
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
Background image
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
Background image
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
Background image
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
Background image
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
Background image
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
Background image
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.
Background image
Image of page 19

You've reached the end of your free preview.

Want to read all 54 pages?

  • Spring '08
  • Xu
  • Continuous function, Limit of a function, Multiplicative inverse, Brett Geiger

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture