- The data suggestthat womenwill reach in 2009;this is unrealisticbasedon currentreportsthat
womenstill lag far behindmen in equalsalariesfor equalwork. - b. Cubic.
c.
d.
- Linear ; Predictedcost in 2012is ; it is hard to say whichmodelworksbest
but it seemsthat the use of a cubicmodelmay overestimatethe cost in the shortterm. - b. ; the amountwill tripleearlyin Year 9.
- a.
b. The amountwill tripleearlyin Year 9 as in the last problembecausethe exponential equations
and both reduce to the same equation
and hencehavethe samesolution. - b.
The Calculus
LearningObjectives
A studentwill be able to:
- Use linearapproximationsto studythe limit process.
- Computeapproximationsfor the slopeof tangentlines to a graph.
- Introduceapplicationsof differentialcalculus.
Introduction
In this lessonwe will beginour discussionof the key conceptsof calculus.Theyinvolvea coupleof basic
situationsthat we will comebackto time and againthroughoutthe book.For eachof these,we will make
use of somebasicideasabouthow we can use straightlines to help approximatefunctions.
Let’s start with an exampleof a simplefunctionto illustrateeachof the situations.
Considerthe quadraticfunction We recallthat its graphis a parabola.Let’s look at the point
on the graph.