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Several other languages use inc(x) and dec(x) functions. The increment operator increases, and the decrement operator decreases, the value of its operand by 1. The operand must have an arithmetic or pointer data type, and must refer to a modifiable data object. Pointers values are increased (or decreased) by an amount that makes them point to ...
The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that. It is valid when and where and may be real or complex numbers. The benefit of this approximation is that is converted from an exponent to a multiplicative factor. This can greatly simplify mathematical expressions (as in ...
Completing the square is used in. solving quadratic equations, deriving the quadratic formula, graphing quadratic functions, evaluating integrals in calculus, such as Gaussian integrals with a linear term in the exponent, [1] finding Laplace transforms. [2][3] In mathematics, completing the square is often applied in any computation involving ...
After a brief stint practicing law for a large international law firm, in 2011 Lidsky partnered with Harvard College roommate Zac Merriman to acquire a small business. They purchased the assets of Orlando Decorative Concrete, Inc. and created ODC Construction, LLC. [9] [10] ODC Construction is a residential shell contractor. It builds the ...
The factor theorem is also used to remove known zeros from a polynomial while leaving all unknown zeros intact, thus producing a lower degree polynomial whose zeros may be easier to find. Abstractly, the method is as follows: [3] Deduce the candidate of zero of the polynomial from its leading coefficient and constant term .
Characterisation 3 involves defining the natural logarithm before the exponential function is defined. First, This means that the natural logarithm of equals the (signed) area under the graph of between and . If , then this area is taken to be negative. Then, is defined as the inverse of , meaning that by the definition of an inverse function.
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
Alexandrova was the Winner of the Russian Regional Student Olympiad in Chemistry in 2000. [1] She attended the Saratov State University for her undergraduate studies, where she was awarded a scholarship from the Government of Russia for outstanding performance in science. She moved to the United States for her graduate studies at Utah State ...