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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?
Two sessions of swimming lessons were held at a pool. In the first session 40 students attended. Of these 40 students 60% were girls.
counting principles please respond to the followingcompare and contrast permutations and distinguishable permutations.
Find the total interest for a loan.
Exhibit that ordered pair which constitutes the vertex. Exhibit the y intercept. How many zeros does this expression have?
Find the vertex,line of symmetry, and the maximum or minimum value of f(x). Graph the function. F(x)= 5 (x+2)2+5 .
Please find a quadratic equation in standard form to model the data in the table. A ball is hit into the air. Its height in feet, s, at time t is given by the equation s(t)=-16^2+25t+4.
The perimeter of a rectangle or field is 340 yards. The length is 50 yards longer than the width. Find the dimensions.The smaller of the two sides is_?_many yd.
Solve the algebraic fraction
Solving quadratic equation
Mary wants to make a line graph to show how the temperature outside changed during the course of one day. She measured the temperature once every hour from 7:00 am to 7:00 pm she records this information in a table.
Solve the given equation using absolute value function.
Could you explain me the easiest steps needed to prove the Holder inequality for L^p spaces?
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