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

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What is Calculus?

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What is calculus

What is Calculus?


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.


What is calculus

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

Numerically

Analytically

Graphically

Verbally


What is calculus

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.


What is calculus

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.


What is calculus

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.


What is calculus

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.


What is calculus

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.


What is calculus

Modeling Data

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

(Source: Bureau of Labor Statistics)


What is calculus

  • Use the regression capabilities of a graphing utility to find a mathematical model of the form y = at2 +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.


What is calculus

(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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