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Oct 26, 2016 · It is said sharp if the equality $a=b$ indeed occurs, so that you cannot find a lower upper bound. For instance, $\sin x\le1$ is sharp; $\sin x\le2$ is true but not sharp. $\endgroup$ –
sharp Often, a mathematical theorem will establish constraints on the behavior of some object; for example, a function will be shown to have an upper or lower bound. The constraint is sharp (sometimes optimal) if it cannot be made more restrictive without failing in some cases.
Dec 16, 2014 · A corner is where the two one-sided derivatives exist, are finite, and are not equal to each other. In the case y =|x| y = | x | the left derivative is −1 − 1 and the right one is 1 1 at x = 0 x = 0. A cusp is where the one-sided derivatives tend to opposite infinities.
- Names of Angles
- Positive and Negative Angles
- Parts of An Angle
- How to Label Angles
As the Angle Increases, the Name Changes:
Try It Yourself: Also: the letter "A" has an acute angle.
When measuring from a line: 1. a positive angle goes counterclockwise(opposite direction that clocks go) 2. a negativeangle goes clockwise
The corner point of an angle is called the vertex And the two straight sides are called arms The angle is the amount of turnbetween each arm.
There are two main ways to label angles: 1. give the angle a name, usually a lower-case letter like a or b, or sometimes a Greek letter like α (alpha) or θ(theta) 2. or by the three letters on the shape that define the angle, with the middle letter being where the angle actually is (its vertex). Example angle "a" is "BAC", and angle "θ" is "BCD"
Oct 29, 2014 · Differentiable functions are locally "linear-like". Zoom in and function and tangent will be more and more similar. But zooming in a sharp turn always gives a sharp turn.
Explore geometry fundamentals, including points, line segments, rays, and lines. Understand dimensions and how these elements form shapes and patterns. Learn key geometric terms like colinear points, midpoints, and vertices, and enhance your knowledge of geometry.
Points, lines and planes underpin almost every other concept in geometry. Angles are formed between two lines starting from a shared point. Shapes, whether two-dimensional or three-dimensional, consist of lines which connect up points.
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