SOLUTION: Consider the rational function p=512500V²-449000v+19307/125v²(1000V-43). Thisos based on the vander Waals equation for predicting the present p of gas as a function of V at a fix
Question 1168446: Consider the rational function p=512500V²-449000v+19307/125v²(1000V-43). Thisos based on the vander Waals equation for predicting the present p of gas as a function of V at a fixed temperature. The function above models the pressure p of carbon dioxide in terms of volume V if the temperature is 500 kelvins.
Process Questions
1. What are the vertical asymptote(s) of function?
2. What is the horizontal asymptote(s) of the function?
3. What are the p- intercept(s) of the function?
4. What is the V- intercept of the function? Answer by solver91311(24713) (Show Source):
In any rational function, you have a vertical asymptote wherever the value of the independent variable makes the denominator function equal to zero unless the factor creating the zero in the denominator creates a zero in the numerator as well.
In a rational function where the degree of the numerator polynomial is less than the degree of the denominator polynomial, the function is asymptotic to the horizontal axis. In a rational function where the degree of the numerator polynomial is equal to the degree of the denominator polynomial, the function is asymptotic to a constant function equal to the quotient of the lead coefficient of the numerator polynomial divided by the lead coefficient of the denominator polynomial. In a rational function where the degree of the numerator polynomial is greater than the degree of the denominator polynomial, there is no horizontal asymptote. There is a slant or oblique asymptote that is a function equal to the polynomial long division quotient of the numerator divided by the denominator excluding any remainder.
The vertical axis intercept is at the value of the function when zero is substituted for the independent variable.
The horizontal axis intercepts are at the zeros of the numerator polynomial.
Your function is improperly stated. V is NOT the same thing as v. Those are two different variables, and I don't believe the Van der Waals equation deals with two different volumes. Yes, I figured out what you meant, but it was rather rude of you to expect me to do that work for you. Proofread your posts BEFORE you send.
John
My calculator said it, I believe it, that settles it
