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What is Calculus?. Calculus is the mathematics of change: Velocity and Acceleration.

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Calculus is the mathematics of change: Velocity and Acceleration.

Calculus is also the mathematics of tangent lines, slopes, areas, volumes, arc lengths, centroids, curvatures, and a variety of other concepts that have enabled scientist, engineers and economists to model real-life problems.


The study of Calculus will be viewed with an approach using the acronym N.A.G.V.

Numerically

Analytically

Graphically

Verbally


Reminder of the acronym x & y-intercepts.

To find an x-intercept plug in a zero for y and solve for x.

To find a y-intercept plug in a zero for x and solve for y.


Symmetry of a graph. the acronym

A graph is symmetric with respect to the y-axis if, (x,y) is a point on the graph and (-x,y) is also a point on the graph.

To test: replace –x in the equation and you should yield the equivalent equation.


Symmetry of a graph. the acronym

A graph is symmetric with respect to the x-axis if, (x,y) is a point on the graph and (x,-y) is also a point on the graph.

To test: replace –y in the equation and you should yield the equivalent equation.


Symmetry of a graph. the acronym

A graph is symmetric with respect to the origin if, (x,y) is a point on the graph and (-x,-y) is also a point on the graph.

To test: replace x with –x, and y with –y in the equation and you should yield the equivalent equation.


Finding points of Intersection the acronym

Graphing is always a great way for realizing how many points of intersection there are. However it might be too time consuming trying to find the proper window. Set the equations equal to each other and solve.


Modeling Data the acronym

The table shows the consumer price index (CPI) for selected years.

(Source: Bureau of Labor Statistics)



(b) Use a graphing utility to graph the model and compare the data with the model.

(c) Use the model to predict the CPI for the year 2004.


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