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In calculus, the power rule is used to differentiate functions of the form , whenever is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function's derivatives .
For example, 10 3 = 1000 and 10 −4 = 0.0001. Exponentiation with base 10 is used in scientific notation to denote large or small numbers. For instance, 299 792 458 m/s (the speed of light in vacuum, in metres per second) can be written as 2.997 924 58 × 10 8 m/s and then approximated as 2.998 × 10 8 m/s.
To the right is the long tail, and to the left are the few that dominate (also known as the 80–20 rule ). In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial ...
Rules. The ten rules are: [1] Avoid complex flow constructs, such as goto and recursion. All loops must have fixed bounds. This prevents runaway code. Avoid heap memory allocation. Restrict functions to a single printed page. Use a minimum of two runtime assertions per function. Restrict the scope of data to the smallest possible.
Generalized power rule. The elementary power rule generalizes considerably. The most general power rule is the functional power rule: for any functions f and g , wherever both sides are well defined. Special cases. If , then when a is any non-zero real number and x is positive. The reciprocal rule may be derived as the special case where .
An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. To round a number to its nearest order of magnitude, one ...
The rule of three is a writing principle which suggests that a trio of entities such as events or characters is more humorous, satisfying, or effective than other numbers. The audience of this form of text is also thereby more likely to remember the information conveyed because having three entities combines both brevity and rhythm with having ...
Home rule in the United States relates to the authority of a constituent part of a U.S. state to exercise powers of governance; i.e.: whether such powers must be specifically delegated to it by the state (typically by legislative action) or are generally implicitly allowed unless specifically denied by state-level action.