Partial Fractions Assignment.sagews

Partial Fractions Assignment

Question 0

Watch the lecture video here.

Did you watch the video? [Type yes or no.]

For each rational function below:

A. Define the function: $\verb|f(x)=...|$

[Make sure you put parentheses around the numerator and denominator, and put a multiplication between each factor in the denominator.]

B. Find the partial fraction decomposition of the function: $\verb|f(x).partial_fraction()|$

C. Integrate each term of the decomposition separately: $\verb|integral(...,x)|$

[Use one line for each term of the decomposition; **do not add these together**.]

D. Integrate the function: $\verb|integral(f(x),x)|$

E. Compare the results of steps C and D.

Question 1

$\displaystyle f(x)=\frac{2x+1}{(x^2+x+1)(x+5)^2}$

Question 2

$\displaystyle f(x)=\frac{4x^3-1}{(x^2-2x+4)^2(3x-7)}$

Question 3

$\displaystyle f(x)=\frac{6x^2+9x-2}{(x+2)^2(x-1)(x^2+5)}$

Question 4

$\displaystyle f(x)=\frac{x^7+x^3+1}{(x-2)(x-3)(x^2+5)}$

[Note: Part of the partial fraction decomposition will be a polynomial. You can integrate the polynomial portion all together.]

This material was developed by Aaron Tresham at the University of Hawaii at Hilo and is
licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.