List of images
Image: The limit of e to the h minus 1 over h is equal to one
A limit involving an exponential is one when the base of the exponential is the number e.
Image: A limit involves many paths in two or more dimensions
In two or more dimensions, one must get the same value along all paths to a point for the limit to exist.
Image: A stretching and flipping two-dimensional linear transformation
A two-dimensional linear transformation that changes orientation and stretches area by a factor of 2.
Image: A stretching two-dimensional linear transformation
A two-dimensional linear transformation that rotates and stretches area by a factor of 4.
Image: Stretching by the linear transformation T(x)=3x
Illustration of stretching by the one-dimensional linear transformation T(x)=3x
Image: Compressing and reflecting by the linear transformation T(x)=-x/2
Illustration of compressing and reflecting by the one-dimensional linear transformation T(x)=-x/2.
Image: The line integral of a conservative vector field
The line integral of a conservative vector field depends only on the endpoints of the curve.
Image: Example line integral over an arc of a circle
A line integral over a quarter unit circle, oriented in the counterclockwise direction.
Image: Example line integral over two line segments
A line integral over a curve composed of two line segments.
Image: A line in two dimensions
The graph of the equation y=3x-2 is a line, if it is an equation in two dimensions.
Image: Line segment path
A straight-line path between two points.
Image: Loggerhead sea turtle
Loggerhead sea turtle
Image: Macroscopic and microscopic circulation
The macroscopic circulation of a vector field around a curve is related to the total microscopic circulation in the interior of the curve.
Image: Macroscopic and microscopic circulation in a region with a hole
The macroscopic circulation of a vector field around both boundary components of a region with a hole is related to the total microscopic circulation in the region.
Image: Metabolic network model for Escherichia coli
Schematic of the metabolic pathways in E. Coli
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