What is Calculus? Calculus is the mathematics of change: Velocity and Acceleration. Calculus is also the mathematics of tangent lines, slopes, areas,

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Presentation transcript:

What is Calculus?

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 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. 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. 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. 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 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 table shows the consumer price index (CPI) for selected years. (Source: Bureau of Labor Statistics) Year CPI

(a)Use the regression capabilities of a graphing utility to find a mathematical model of the form y = at 2 +bt + c for the data. In the model, y represents the consumer price index and t represents the year, with t = 0 corresponding to 1970.

(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.