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Zeros between two significant non-zero digits are significant (significant trapped zeros). 101.12003 consists of eight significant figures if the resolution is to 0.00001. 125.340006 has seven significant figures if the resolution is to 0.0001: 1, 2, 5, 3, 4, 0, and 0. Zeros to the left of the first non-zero digit (leading zeros) are not ...
A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator. The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the relative degree of the transfer function.
If the discriminant is equal to zero, there will be two coinciding real solutions at −b/2a. Finally, if the discriminant is greater than zero, there will be two real negative solutions, because b 2 − 4 a c < b {\displaystyle {\sqrt {b^{2}-4ac}}<b} for positive a , b and c .
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region with closed contour , if |g(z)| < |f(z)| on , then f and f + g have the same number of zeros inside , where each zero is counted as many times as its multiplicity.
Let f be a continuous function for which one knows an interval [a, b] such that f(a) and f(b) have opposite signs (a bracket). Let c = (a +b)/2 be the middle of the interval (the midpoint or the point that bisects the interval). Then either f(a) and f(c), or f(c) and f(b) have opposite
Most commonly the absolute percent errors are weighted by the actuals (e.g. in case of sales forecasting, errors are weighted by sales volume). [3] Effectively, this overcomes the 'infinite error' issue. [ 4 ]
In fact, a gallon of 2% has more than half the fat as a gallon of whole milk. The FDA requires whole milk to have at least 3.25$ fat by weight. But the amount of fat can range from 3.25$ to 5 ...
The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities. [3]