CK12 Calculus - Single Variable

Single Variable Calculus ...

CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both i ...

Authors RajaAlmukkahal,VictorCifarelli,Chun-TakFan,and LouiseJarvis. Supportedby CK-12 Foundation iii ...

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Contents Functions,Limits,and Continuity..................................................................................... ...

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1. Functions,Limits,and Continuity.............................................................................................. ...

We call this shapea parabolaand everyquadraticfunction, has a parabola- shapedgraph.Let’s recallhow we analyticallyfind the key ...

Let’s look at a coupleof moreexamples. Example2: Hereare someotherexamplesof equationswith their correspondinggraphs: ...

Example3: We recallthe first equationas linearso that its graphis a straightline. Can you determinethe intercepts? Solution: -in ...

Sometimeswe wish to look at pairsof equationsand examinewherethey havecommonsolutions.Consider the linearand quadraticgraphsof t ...

The cost to ride the commutertrain in Chicagois. Commutershavethe optionof buyinga monthly couponbookcosting that allowsthemto r ...

We can representthe graphof the relationshipusingour graphingcalculator. The vertexis the maximumpointon the graphand is located ...

3. 4. ...

Oncea car is drivenoff of the dealershiplot, it losesa significantamountof its resalevalue.The graph belowshowsthe depreciatedv ...

A rectangularswimmingpool has lengththat is yardsgreaterthan its width. a. Give the area enclosedby the pool as a functionof it ...

b. c. becauseyou wouldexpect(1) a declineas soonas you boughtthe car, and (2) the valueto be declining moregraduallyafter the i ...

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Of these,the circlehas a qualitythat the othergraphsdo not share.Do you knowwhatit is? Solution: The circle’s graphincludespoint ...

Let’s startwith the notationwe use to describefunctions.Considerthe exampleof the linearfunction We couldalso describethe functi ...