Partial fractions (HSC SSCE Mathematics Extension 2): Flashcards
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What is a rational function?
What is a rational function?
A function as the quotient of two polynomials.
What is partial fraction decomposition?
What is partial fraction decomposition?
Expressing a rational function as simpler fractions.
Why are partial fractions important in calculus?
Why are partial fractions important in calculus?
They simplify the integration of rational functions.
How do you start decomposing a rational function?
How do you start decomposing a rational function?
Set it as a sum of simpler fractions with unknowns.
What are linear factors in partial fractions?
What are linear factors in partial fractions?
Factors like (x-a) used in decomposition.
What defines equality of two polynomials?
What defines equality of two polynomials?
They are equal if their corresponding coefficients match.
What methods find coefficients in partial fractions?
What methods find coefficients in partial fractions?
Equating coefficients and substitution method.
How do you integrate using partial fractions?
How do you integrate using partial fractions?
Decompose, then integrate each simpler component.
How to simplify expressions with quadratic denominators?
How to simplify expressions with quadratic denominators?
Factor the denominator and use partial fractions.
What is a special case in partial fractions?
What is a special case in partial fractions?
Repeated application may be needed for some functions.