Exam 3

Question 1

Partial fraction steps

Answer 1

factor denominator
partial fraction decomp
clear denominator
solve for coefficients

use smart substitution

Question 2

Partial fractions if part doesn’t decompose

Answer 2

put ax+b on top

Question 3

Partial fractions for repeated linear terms

Answer 3

increase power of the thing on bottom

Question 4

simple irreducible quadratic factor
ax^2+bx+c

Answer 4

(ax+b)/ax^2+bx+c

Question 5

T or F repeated irreducible quadratic factors have the same thing on top

Answer 5

false the ax+b is different

Question 6

error for midpoint equation

Answer 6

M is highest goalie is f’’

error in M <= K(b-a)^3/24n^2

Question 7

midpoint equation

Answer 7

f(m.n)dx +f(m.n+1)dx

Question 8

trapezoid rule

Answer 8

1/2 * dx (f(x.1) + 2f(x.2) +f(x.3))

Question 9

error bounds for trapezoid

Answer 9

M is f” highest value

error in T.n <= K(b-a)^3 / 12n^2

Question 10

simpson rule

Answer 10

1/3 * dx (f(x.1) + 4f(x.2) +2f(x.3)+ 4f(x.1) + 2f(x.2) +4 (x.3) + f(x.4) )

Question 11

error in simpsons

Answer 11

M is highest value in f””

error in s <= M(b-a)^5 / 180n^4

Question 12

Comparison theorem

Answer 12

if one function is bigger than the other in same magnitude and bigger one converges smaller also converges

Question 13

general solution to a first order linear equation y’(t) =ky +b

Answer 13

y = Ce^kt -b/k

Question 14

what is separable

Answer 14

g(y) y’(t) = h(t)