CK12 Calculus - Single Variable

6.052.0125 2.0124 2.0124

As you can see from the graphbelow, is an excellentapproximationof near

We get a slightlybetterapproximationfor the quadraticthan for the linear. If we reflecton this a bit, the
findingmakessensesincethe shapeand propertiesof quadraticfunctionsmorecloselyapproximatethe
shapeof radicalfunctions.
Finally, as in the first example,we wish to determinethe rangeof valuesthat will ensurethat our approx-
imationsare within of the actualvalue.Usingthe TABLE featureof the calculator, we find that if
then.

LessonSummary

1. We extendedthe MeanValue Theoremto makelinearapproximations.


2. We analyzederrorsin linearapproximations.


3. We extendedthe MeanValue Theoremto makequadraticapproximations.


4. We analyzederrorsin quadraticapproximations.

ReviewQuestions

In problems#1–4,find the linearization of the functionat

1. near


2. on


3. Find the linearizationof the function near a = 1 and use it to approximate.


4. Basedon usinglinearapproximations,is the followingapproximationreasonable?


5. Use a linearapproximationto approximatethe following: