Partial Fractions: Problem 2
Use the method of partial fraction decomposition to write the
following rational expression as the sum of simpler rational
functions whose denominators are polynomials of degree 1.
−20x+20/x^2−x−56=
Once you have a system of equations generated by the partial fraction decomposition, can you explain another method to solve it? For example if you hadwe eventually simplify to 7x + 13 = A(3x + 5) + B(x+1). Explain how you could intelligently choose an x-value that will eliminate either A or B and solve for A and B.
Write a class named Rat (to simulate rational or fraction
number) such that it works as in the main below.
int main()
{
Rat a(3, 4), b(1, 2);
a.print(); // output: 3/4
b.print(); // output: 1/2
Rat c = a.add(b);
c.print(); // output: 5/4
// Hint: 3/4 + 1/2 = 6/8 + 4/8 = 10/8 = 5/4
Rat d = a.multiply(b);
d.print(); // output: 3/8
// Hint: 3/4 x 1/2 = 3/8
return 0;
}
Write the expression as an equivalent expression in the form x^n.
Simplify your answer as much as possible, and enter your answer as
a fraction.
(X^6)^4/(X^6)(X^4)
2. Convert the following infix form expression into the postfix
form expression by using a stack:
A+(B*(C-D)+E)/F-G*H
Show the stack after each push/pop.
1.) use partial fractions to decompose each into a fraction with
a linear factor in the denominator:
a.) 2/(x+1)(x+2)
b.) 2/(y)(100-y)
c.) y/(y)(100-y)
d.) 5/x(x+1)(x-2)
e.) 2x+3/x(x+1)(x-2)
f.) x^2/x(x+1)(x-2)
2. Consider the ODE model for population growth:
a. Use separation of variables to determine the solution.
b. What is the value of y(1)?
c. What is the value of y(10)?
d. At what time will the population reach 100? At what time will
it reach 1000?
3. Consider the logistic...