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For example, using single-precision IEEE arithmetic, if x = −2 −149, then x/2 underflows to −0, and dividing 1 by this result produces 1/(x/2) = −∞. The exact result −2 150 is too large to represent as a single-precision number, so an infinity of the same sign is used instead to indicate overflow.
Defining 0 0 = 1 is necessary for many polynomial identities. For example, the binomial theorem (+) = = holds for x = 0 only if 0 0 = 1. [4] Similarly, rings of power series require x 0 to be defined as 1 for all specializations of x.
7.4 Reciprocal of tetrahedral numbers. 7.5 Exponential and logarithms. 8 See also. ... Text is available under the Creative Commons Attribution-ShareAlike 4.0 License
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
For example, we may say (+) = because for every real ε > 0, we can take δ = ε/4, so that for all real x, if 0 < | x − 2 | < δ, then | 4x + 1 − 9 | < ε. A more general definition applies for functions defined on subsets of the real line. Let S be a subset of .
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The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.