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These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
Artificial intelligence (AI), in its broadest sense, is intelligence exhibited by machines, particularly computer systems.It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximize their chances of achieving defined goals. [1]
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [ 1] As an example, " is less than " is a relation on the set of natural numbers; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
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The U.S. Border Patrol later reported that over 1.3 million people (a number viewed by many to be inflated) were deported or left the U.S. voluntarily under the threat of deportation in 1954. [178] [180] Meanwhile, the number of Mexicans immigrating legally from Mexico grew rapidly during this period, from 18,454 in 1953 to 65,047 in 1956. [178]
4. Professional Mourner. Pay: $28,000 per year. This seems sad for many reasons, but if no one is going to a funeral you're overseeing, you can hire someone to sit in (and, in the case of ...
Integral. In integral calculus, integration by reduction formulae is a method relying on recurrence relations. It is used when an expression containing an integer parameter, usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree, can't be integrated directly. But using ...
A control-Lyapunov function (CLF) is a function that is continuously differentiable, positive-definite (that is, is positive for all except at where it is zero), and such that for all there exists such that. where denotes the inner product of . The last condition is the key condition; in words it says that for each state x we can find a control ...