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The reason why polynomials are so important is that there is a theorem from Analysis that says that any continuous function defined on an interval of the real line can be approximated arbitrarily closely by a polynomial. So polynomials are useful to ¿model¿ any kind of function on a closed interval. However, polynomials ¿get wild¿ at infinity, so they don¿t work well to try to extrapolate an arbitrary function past the closed interval in which it is being approximated by the polynomial.
A rational function is a function which is a ratio of two polynomials, one polynomial in the numerator and another one in the denominator. Rational functions are also used to model an arbitrary function, and for many purposes they have better behavior. If the rational function is a ratio of two polynomials of the form p(x)/q(x), and the order of the two polynomials is np and nq, try to give a qualitative description of the behavior of this rational function. What happens to the rational function in the cases np > nq, np = nq, and np < nq as x goes to plus or minus infinity (compare with the case of a polynomial)? If an arbitrary function f(x) goes to zero at plus and minus infinity, what kind of rational function would be best to model this function?
Find the equation of this line in slope-intercept form. If Bob's salary trend continued, what would his salary be in the year 2005?
Estimate the slope of the equation.
to win a prize a person must select 3 numbers from 13 numbers. find the probability of winning if a person buys one
Fields are an important algebraic structure, and complex numbers have that structure - verify that the fifth roots of unity form a group under complex multiplication, showing all work.
A random sample of 91 employees of Eastern Electric Co. showed that the number of days missed by each worker last year due to illness was as follows:
A system of three linear equations in three unknowns has a unique solution if and only if its coefficient matrix is row equivalent to the 3x3 identity matrix.
Perform the computations and write your answer in scientific notation.
Make the number in standard notation
Find the equation of the function
What are the values of the companies as stand-alone companies? If the combined firm increases its operating margin by 2%, revenues are combined, and the other value drivers remain unchanged, what is the value of the combined firm?
A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100ft of fence? What should the dimensions of the garden be to give this area?
A health club asked the dietitian to prepare 600 ounces of a nutritional drink containing 5.5 grams of carbohydrates per ounces. The dietitian has a nutritional drink containing 5.0 grams per ounces & one that contains 5.8 grams of carbohydrate per o..
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