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Thomas a.k.a. Taz Kostielney
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Section 1.1 By: Thomas a.k.a. Taz Kostielney Thomas a.k.a. Roadrunner Krcmaric Chris a.k.a. Eagle Hoffman What is Calculus? The mathematics of change, such as ... – PowerPoint PPT presentation
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Title: Thomas a.k.a. Taz Kostielney
1
Section 1.1
- By
- Thomas a.k.a. Taz Kostielney
- Thomas a.k.a. Roadrunner Krcmaric
- Chris a.k.a. Eagle Hoffman
2
What is Calculus?
- The mathematics of change, such as velocities and
accelerations. - Calculus allows people to model real life
situations.
3
Calculus Basics
- There are two types of calculus differential,
the rate of change of something, and integral,
which, among other things, is used to find the
area under a curve.
4
When you do not need to use Calculus
- when finding
- The slope of a line
- Secant line to a curve
- Curve of a circle
- Height of a curve at a specific point
- Tangent plane to a sphere
- Direction of motion on a straight line
- Average rate of change between two points
5
When you do not need to use Calculus
- Finding the area of a rectangle
- Work done by a constant force
- Finding the center of a rectangle
- Length of a line segment
- Volume of a rectangular solid
- Sum of a finite number of terms
- Surface area of a cylinder
6
When you need Calculus
- when finding
- Slope of a curve
- Tangent line to a curve or surface
- Instantaneous rate of change at a particular time
- Curvature of a curve
- Maximum height of a curve on an interval
- Direction of motion on a curve
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When you need Calculus
- Area under a curve
- Work done by a variable force
- Length of an arc
- Surface area of a solid of revolution
- Mass of a solid with variable density
- Volume of a region under a surface
- Sum of an infinite number of terms
8
Tangent Line Problem
- Limits are a fundamental part of Calculus.
- You will be given a function and a point (c,
f(c)) on that function. You want to find the
tangent line at that particular point. - Draw a secant line through the given point and
another point (c?x, f(c?x)) on the curve.
9
Tangent Line Problem
- The slope of the tangent line is the limit of the
slope of the secant line. (Dont worry, this will
all make sense to you when you actually do this.) - Slope of the secant
- (Doesnt that look pretty)
- Slope of the tangent
10
The Area Problem
- To find the area of a region under a curve, you
place rectangles on the curve to the x-axis. - Adding the rectangles areas approximates the
overall area. - The more rectangles, the more accurate the
approximation. - Apply a limit as the number of rectangles
approaches infinity.
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THE END..
