Class Notes (807,726)
United States (312,770)
Mathematics (425)
MTH 162 (75)
Pachero (61)
Lecture 11

MTH 162 Lecture 11: 6.3 Partial Fractions Notes

4 Pages
Unlock Document

University of Miami
MTH 162

MTH 162 Calculus II 6.3 Partial Fractions Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section. Rational Functions p(x) ▯ Rational functions are functions that are in the common form of R(x) = q(x) which shows where both p(x) and q(x) are polynomial functions while it’s only q(x) can’t be a zero polynomial. – This would generally mean the following: q (x) 6= 0 ▯ When you are trying to figure out the domain, besides that fact that q (x) 6= 0, then you find out that it [the domain] will be all real numbers. ▯ If you have any rational function that is in the general form of R(x) = q(x) in its lowest form, then you’ll have R will have a vertical asymptote for each and every value of x for which q(x) = 0. Steps to Partial Fractions ▯ Partial fractions deals with writing ration functions as the sum of the simpler fractions and these are the steps to partial fractions: – These are the steps when the rational function is actually while it’s numerator’s degree is less than the denominator’s degree: ▯ Factor q(x), which is the denominator. ▯ Create a sum of fractions with the all of the numerators are all different variables with the denominators are actually each of those factors. ▯ Create fractions with factor’s increasing powers in there are any repeated factors. ▯ Multiply by q(x), which is the denominator. ▯ Set the numerator, which is p(x), to 0. ▯ Solve for all variables. – These are the steps when the rational function is actually while it’s numerator’s degree is greater than the denominator’s degree: ▯ Perform any long division that can come in the form of the following: p(x) = f (x) + r (x) q (x) q (x) r(x) ▯ Find the remainder’s, which is q(x) partial function. 1 Partial Fraction Example: Decomposing Decompose the following into partial functions: x R(x) = (x + 1)(x ▯ 4) x (x+1)(x▯4) x a0 a1 (x▯4)(x+1)= x▯4+ x+1 x(x▯4)(x+1) a0(x▯4)(x+1) a1(x▯4)(x+1) (x▯4)(x+1) = x▯4 + x+1 x = a0(x + 1) + a1(x ▯ 4) (▯1) = a0((▯1) + 1) + a1((▯1) ▯ 4) ▯1 = a (0) + a (▯5) 0 1 ▯1 = ▯5a 1 ▯1 ▯5a ▯5 = ▯51 1 a1= 5 x = a0(x + 1) + a1(x ▯ 4) 4 = a0(1 + 4) + a1(4 ▯ 4) 4 = a0(5) + a1(0) 4 = 5a 0 4= 5a0 5 4 a0= 5
More Less

Related notes for MTH 162

Log In


Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.